a 60- kg mountain climber moves 10 m up a vertical slope. if the muscles in her body convert chemical energy into gravitational potential energy with an efficiency of no more than 5%, what is the chemical energy used to climb the slope?

Answers

Answer 1

120000 Joules of Chemical Energy is used by the climber to climb the rope.

As the climber is moving up, its gravitation potential energy energy (G) will be given by,

Gravitational potential Energy = MgH

G = MgH

Where,

M is mass of climber which is 69 Kg,

g is acceleration due to gravity which is 10m/s².

H is the height above the earth's surface which is 10 meters.

It is provided that the chemical energy is converted to gravitational energy at a rate of 5%.

So, we can write,

5% Chemical energy (C) = Gravitational potential energy (G)

So,

5%C = MgH

Putting all the values,

5C/100 = 60(10)(10)

C = 120000 Joules.

The used chemical energy is 120000 Joules.

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Related Questions

A 6-kg bowling ball rolling at 5 m/s strikes a stationary 4-kg bowling ball. If Ball #1 is moving forward at 2 m/s after the collision, what is the speed and direction of Ball #2?​

Answers

The speed of ball #2 after the collision will be 4.5 m/s.

Given,

The mass of ball 1 = 6kg

The mass of ball 2 = 4 kg

Initial speed of ball 1 = 5 m/s

Final speed of ball 1 = 2 m/s

Initial speed of ball 2 = 0 m/s

Let us suppose the final speed of ball 2 is x m/s.

We know that, from the conservation of momentum theorem:

m1.v1(initial) + m2.v2(initial) = m1.v1(final) + m2.v2(final)

6.5 + 4.0 = 6.2 + 4.x

30 + 0 = 12 + 4x

=>4x = 18

=> x = 4.5 m/s

Thus the speed of 2nd ball after the collision will be 4.5 m/s.

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You are driving at the speed of 29.5 m/s
(66.0037 mph) when suddenly the car in
front of you (previously traveling at the same
speed) brakes and begins to slow down with
the largest deceleration possible without skidding. Considering an average human reaction,
you press your brakes 0.558 s later. You also
brake and decelerate as rapidly as possible
without skidding. Assume that the coefficient
of static friction is 0.708 between both cars’
wheels and the road.
The acceleration of gravity is 9.8 m/s
2
.
Calculate the acceleration of the car in front
of you when it brakes.
Answer in units of m/s
2
.
What is the frictional force acting on the
35 kg mass?
Answer in units of N

Answers

Answer:

honestly not sure what to do good luck though

Please help, I have no idea what story I can make out of these..

Make up a short story that uses these three constellations: Orion, Taurus, and Canis Major

Thank you!

Answers

Constellation is a group of stars that appears to form a pattern or picture. Some of the constellations include Orion, Taurus, Canis Major etc.

Orion is located on the celestial equator and it can be seen throughout the world. This constellation is named after the hunter, in Greek mythology. It is one of the most obvious and recognizable constellations in the sky. Orion is most visible in the evening sky from January to April, during winter season in the Northern Hemisphere, and summer season in the Southern Hemisphere. In the tropics, the constellation moves at the zenith. Orion is bordered by Taurus to the northwest, and by other constellations in other directions.

Taurus is one of the constellations of the 12 zodiac signs. It is a large and prominent constellation in the Northern Hemisphere during winter. It is one of the oldest constellations. The International Astronomical Union gave a three-letter abbreviation for the constellation, as "Tau". During late November-early December, Taurus occupies a furthest point from the Sun and is visible the entire night. By late March, it sets at sunset and completely disappears behind the Sun's glare from May to July.

Canis Major is a constellation in the southern celestial hemisphere. It is a Latin name, which means 'greater dog' in contrast to 'Canis Minor' meaning 'lesser dog'. These both figures are commonly represented as following the constellation of Orion, the hunter, through the sky. Canis Major contains Sirius, the brightest star in the night sky, known as the "dog star". It is bright because of its proximity to the Solar System.

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(1 point) suppose a spring with spring constant 8 n/m is horizontal and has one end attached to a wall and the other end attached to a mass. you want to use the spring to weigh items. you put the spring into motion and find the frequency to be 0.9 hz (cycles per second). what is the mass? assume there is no friction. mass

Answers

According to the given statement The mass attached to the spring is 3.99 kg.

What is Spring mass system ?

A spring system with a block hanging from or affixed to the spring's free end is known as a spring-mass system. The spring-mass system is typically used to calculate the duration of any object in a simple harmonic motion.

Briefing:

F = -kx

where k is the spring constant, and

x is the displacement of the spring

The angular frequency of the spring is:

[tex]\omega=\sqrt{\frac{k}{m}}[/tex]

m is the mass of object attached to the spring

So, frequency:

f = ω/2π = [tex]\frac{1}{2 \pi} \sqrt{\frac{k}{m}}[/tex]

m = 4π²f² / k

given that f = 0.9 Hz, and

k = 9 N/m

m = (4×π²×0.9²)/8

m = 3.99 kg

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An explanation for planetary differentiation is_____________. question 5 options: all the planets are different colors and some have life, while others do not different scientist are chosen to explore planet similarities is the separation of different constituents of planetary materials resulting in the formation of distinct compositional layers. denser material tends to sink into the center and less dense material rises toward the surface. planets have different orbits around the sun and therefore consist of varying elements

Answers

One hypothesis for planetary differentiation is the process through which various layers with diverse chemical and/or physical features arise.

A planet's trajectory around a star, a natural satellite's path around a planet, or an artificial satellite's course around a space object or place, such as a planet, moon, asteroid, or Lagrange point, are examples of orbits in celestial mechanics.

A spacecraft, planet, moon, star, or other object travels on a curved route called an orbit when it is dragged by the gravity of another object.

The force of gravity is what pulls objects with mass in space. An orbit is a path an object follows as it travels around a certain location in space, such as the Moon's orbit of the Earth.

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Tamara is playing a game of billiards. The white cue ball has a mass of 0.17 kg and all the other balls have a mass of 0.16 kg. The cue ball is moving at a velocity of 6 m/s when it collides with the number seven ball. If the cue ball comes to a complete stop after the collision, then what will the resulting velocity be on the number seven ball?

Answers

Tamara is playing a game of billiards. The white cue ball has a mass of 0.17 kg and all the other balls have a mass of 0.16 kg. The cue ball is moving at a velocity of 6 m/s when it collides with the number seven ball. If the cue ball comes to a complete stop after the collision, then the resulting velocity of the number seven ball  will be 6.375 m/s

The law of conservation of momentum states that, within some problem domain, the amount of momentum remains constant; momentum is neither created nor destroyed, but only changed through the action of forces as described by Newton's laws of motion.

using law of conservation of momentum

initial momentum of the system  = final momentum of the system

m1u1 + m2u2 = m1v1 + m2v2                          equation 1

m1 = mass of cue ball

u1 = initial velocity of cue ball

m2 = mass of number seven ball

u2 = initial velocity of number seven ball

v1 =  final velocity of cue ball

v2 =  final velocity of number seven ball

substituting in equation 1

(0.17 * 6) + ( 0.16 * 0 ) = (0.17 * 0) + ( 0.16 *  v2)

v2 = 6.375 m/s

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suppose a 62-turn coil lies in the plane of the page in a uniform magnetic field that is directed into the page. the coil originally has an area of 0.25 m2. it is stretched to have no area in 0.100 s. what is the magnitude of the induced emf (in volts) if the uniform magnetic field has a strength of 1.50 t?

Answers

The magnitude of electromotive force is 232.5 volts.

We need to know about the electromotive force of induction to solve this problem. The emf induction appears when there is any change in magnetic flux. The magnitude of emf can be determined by

ε = N dΦ / dt

where N is coil turns, ε is electromotive force, dΦ is change in magnetic flux and dt is time interval.

From the question above, the parameters given are

N = 62

A/t = 0.25 m² / 0.1 s

t = 0.1 s

B = 1.5 T

By substituting the given parameters, we can calculate electromotive force

ε = N . dΦ / dt

ε = 62 . B . A / t

ε = 62 . 1.5 . 0.25 / 0.1

ε = 232.5 volts

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You want to lift a heavy box with a mass L = 64.0 kg using the two-ideal pulley system as shown. With what minimum force do you have to pull down on the rope in order to lift the box at a constant velocity? One pulley is attached to the ceiling and one to the box.

Answers

The given problem can be solved using the following free-body diagram:

The diagram is the free-body diagram for the pulley that is holding the weight. Where:

[tex]\begin{gathered} T=\text{ tension} \\ m=\text{ mass} \\ g=\text{ acceleration of gravity} \end{gathered}[/tex]

Now we add the forces in the vertical direction:

[tex]\Sigma F_v=T+T-mg[/tex]

Adding like terms:

[tex]\Sigma F_v=2T-mg[/tex]

Now, since the velocity is constant this means that the acceleration is zero and therefore the sum of forces is zero:

[tex]2T-mg=0[/tex]

Now we solve for "T" by adding "mg" from both sides:

[tex]2T=mg[/tex]

Now we divide both sides by 2:

[tex]T=\frac{mg}{2}[/tex]

Now we substitute the values and we get:

[tex]T=\frac{(64\operatorname{kg})(9.8\frac{m}{s^2})}{2}[/tex]

Solving the operations:

[tex]T=313.6N[/tex]

Now we use the free body diagram for the second pulley:

Now we add the forces in the vertical direction:

[tex]\Sigma F_v=T-F[/tex]

The forces add up to zero because the velocity is constant and the acceleration is zero:

[tex]T-F=0[/tex]

Solving for the force:

[tex]T=F[/tex]

Therefore, the pulling force is equal to the tension we determined previously and therefore is:

[tex]F=313.6N[/tex]

An elevator uses 100 000J of electrical energy to raise a load of 800 N through a height of 40m in a time of 20s. What is the rate of conversion of the electrical energy to other forms?

Answers

[tex]W_{out}=F\cdot d=800\cdot40=32000[/tex][tex]P_{out}=\frac{W_{out}}{t}=\frac{32000}{20}=1600W[/tex][tex]\begin{gathered} P_{in}=\frac{W_{in}}{t}=\frac{100000}{20}=5000W \\ \end{gathered}[/tex]

Therefore:

[tex]P_{out}:P_{in}=\frac{P_{out}}{P_{in}}=\frac{1600W}{5000W}=0.32[/tex]

Answer:

1600W

when 1 kg of water and 1 kg of wood absorb the same amount of heat, the change in temperature of water is less than the changes in temperature of the wood. which statement helps to explain this difference?
A. The latent heat of fusion of water is less than of wood.
B. Intermolecular forces in water are less than those in wood.
C. Intermolecular forces in water are greater than those in wood.
D. The latent heat of fusion of water is greater than that of wood.

Answers

When 1 kg of water and 1 kg of wood absorb the same amount of heat, the change in the temperature of the water is less than the change in temperature of the wood because the intermolecular forces in water are greater than those in wood.

What are intermolecular forces?

Intermolecular forces are the forces of attraction that exist between the molecules of the same substance.

Intermolecular forces help to keep the molecules of a substance.

The stronger the intermolecular forces between molecules of a substance, the more heat energy it will require to separate the molecules of the substance.

The molecules of water have in addition to the covalent bond between the atoms of hydrogen, hydrogen bonds that exists between its molecules.

These intermolecular forces present in water are responsible for the high heat capacity of water.

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a 500 gram stone tied to the end of 1.2 m cord is swung into a vertical circular motion with a radius equal to the cord length. find the speed of the stone at the bottom of the circle if the tension in the cord is three times the stone's weight.

Answers

The speed of the stone at the bottom of the circle is 4.85 ms⁻¹.

Speed is the time fee at which an object is moving alongside a course, even as the pace is the charge and path of an object's movement. The rate of speed of the function of an object in any course.

velocity is measured because of the ratio of distance to the time in which the space became blanketed. the pace is a scalar amount because it has the most effective route and no magnitude. Speed is the time fee at which an object is moving alongside a path, while the pace is the fee and direction of an item's motion. put another way, the pace is a scalar value, whilst pace is a vector.

At the bottom position,

T - mg = Fc = mv²/r

∴ (T - mg/m)r = v²

V² = (3mg - mg ) r/ m = 2mgr/m

v = [tex]\sqrt{2gr}[/tex]

   = 4.85 ms⁻¹

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suppose your friend tells you that light from the nearest star, alpha centauri, requires a time of about 4.37 light-years to reach the earth. what is incorrect about this statement? explain your reasoning

Answers

The statement is incorrect about the light year .

What is a light year ?

A Light year is the distance that light travels in a vacuum in one year.

The fastest thing we know is light, which travels through empty space at 186,000 miles or 300,000 kilometers per second. To give you an idea of ​​how fast it is, light can circle the Earth about seven times in one second. Astronomers use the speed of light to measure distance in space. A light year (ly) is the distance that light can travel in one year. In one year, light travels approximately 5,880,000,000,000 miles or 9,460,000,000,000 kilometers. So this distance is 1 light year. For example, our closest star is about 4.3 light years away. Our galaxy, the Milky Way, is about 150,000 light-years across, and the nearest large galaxy, the Andromeda Galaxy, is 2.3 million light-years away from her.

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What is Amy's distance and displacement if she runs 2 miles south, then turns around and runs 3 miles north?

Answers

Amy's distance and displacement if she runs 2 miles south, then turns around and runs 3 miles north is 1 mile.

What is Displacement?

This is referred to as the change in the position of an object and it is usually measured in meters by finding the difference in location between the two bodies involved.

We were told that she runs 2 miles south, then turns around and runs 3 miles north and they are at exact opposite sides on the map which means that the displacement will be:

3 miles - 2 miles

= 1 mile hence, it is the correct choice.

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Find the x-component of this
vector:
12.1 m
48.4°

Answers

The resultant distance of the vector is 12.1 m and the angle between two vectors are 48.4°. So the x-component of this vector is, Aₓ = 8.0335 m

What is vector?

Vector is a product that means a parameter has two types of property one is value second is direction. If a parameter has both then it called a vector quantity. Example: Velocity.

How can we calculate x-component of this vector?

To calculate the vector we know first this is a proper vector quantity or not. According to the question, this is a vector quantity. So it has two component, one along x axis another is y axis as shown in the picture.

We have to calculate the x-component, so we are using the formula is,

Aₓ = Acosθ

Here we are given,

A = The resultant distance of the vector = 12.1 m

θ= The angle between two vectors = 48.4°.

Now We have to calculate the x-component = Aₓ

Now we put the known values in the above equation, we get

Aₓ = Acosθ

Or, Aₓ = 12.1*cos(48.4°)

Or, Aₓ = 8.0335 m

According to the calculation we get, the x-component of this vector is, Aₓ = 8.0335 m

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Answer:

Explanation:

hey the top of me tried there hardest to find you all a answer instead of saying the person who posted this left a blank so what its just a blank stop being so rude to them they are just trying to help and they helped me on my work that i done so don't be so rude because there just trying there hardest!! :)

an ideal parallel-plate capacitor consists of a set of two parallel plates of area a separated by a very small distance d. when the capacitor plates carry charges q and -q, the capacitor stores energy u0. if the separation between the plates is doubled, how much electrical energy is stored in the capacitor?

Answers

Electrical energy is energy that has to do with forces acting on electrically charged particles and their motion.

What is mean by electrical energy?

The ability of an atom's charged particles to initiate an activity or move an object is known as electrical energy. Electrical energy is produced by the transfer of electrons between atoms. Electrical energy powers your toaster and phone charger every time you plug them into a wall outlet.

Electrical energy is energy that has to do with forces acting on electrically charged particles and their motion.

The capacitance of a capacitor is given by the following formula

C=∑0A/d

And the electric potential energy stored in a capacitor is given by

∪[tex]Q2[/tex]/2AC

Applying these formula to the given variables, the initial potential energy becomes

∪[tex]0[/tex]=[tex]Q2/2=d/[/tex]∑A

If d becomes 2d, then potential energy becomes

∪0=[tex]Q2/2[/tex] 2D/∑A=2∪0

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When resistors are put in series next to each other, their overall resistance isA. Larger than that of any individual resistorB.the same as the resistance of one of the resistorsC. Smaller than the resistance of any of the resistors

Answers

Answer:

A. Larger than that of any individual resistor

Explanation:

When resistors are put in series, the overall resistance is equal to the sum of all the resistances. So, the overall resistance will be larger than that of any individual resistor.

Physics Question A ball of Mass 4. 0kg Moving at 6m5' collided with a vertical wall, and retraces its path in the opposite direction at 3 ms: If the time of impact is 0. 20g, Calculate:
1. Magnitude of the change in the linear momentum of the bofy.
ii magnitude of the loss in the Kinetic energy. Iii magnitude of the force experienced by the body due to collision with the ball. ​

Answers

The ball experiences an equal and opposing force from the wall as a result of Newton's third law .Therefore, in a perfect world, the ball would return at the same speed it originally did, preserving momentum.

   explain magnitude of the loss in the Kinetic energy?

An object's mass times its velocity change equals the change in momentum of that object.Δp=m⋅(Δv)=m⋅(vf−vi) Pi=m1v1 will be the system's initial momentum.Therefore, the difference between the initial and final kinetic energies is non-zero, demonstrating that kinetic energy is always lost in inelastic collisions. The magnitude of this loss is Loss=12m1v12[m2m1+m2]. The ball is severely deformed as it is struck due to the bat's tremendous force.The average force acting during the bat-ball collision is therefore about two tons, with a peak force of nearly four tons, during the 0.7 millisecond contact time. By multiplying the magnitudes of two forces acting in the same direction along a straight line, you can quickly calculate the combined force.

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A force of 10 n stretches a particular spring by 2 cm. How far would a 20 n force stretch that same spring?.

Answers

x2 = 4cm.

20N stretches the same spring 4cm.

What is Hooke's law?The displacement or size of a deformed object is directly proportional to the deforming force or load for relatively small deformations.The spring constant k, is a measure of the spring's stiffness. It varies depending on the spring and material. The greater the spring constant, the stiffer the spring and more difficult to stretch.

The force exerted on the spring, F1 = 10N

In the spring, 1st stretch, x1 = 2cm

The force exerted on the spring, F2 = 20N

In the spring, 2ns stretch, x2 = ?

We have to find x2,

The spring constant value for the same spring must be the same. Hooke's law expresses the relationship between force and spring constant as follows:

F=kx.

F1/x1 = F2/x2

By substituting values,

10 / 2 = 20 / x2

x2 = 40/10

x2 = 4cm

As a result, the 20 N force stretches by 4 cm.

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a projectile is launched horizontally with a speed of 80.0 m/s. if the projectile is launched from a hihg of 1.5 meter above the floor, how long does it take the projectile to hit ht efloor

Answers

The time taken by the projectile to hit the floor is 0.55 s.

What is projectile motion?

The projectile motion refers to the motion of an object or particle that is launched into a gravitational field, such as from the surface of the Earth, and travels along a curved path while only being influenced by gravity. A body is considered to be in projectile motion if it moves both vertically and horizontally (trajectory) from the point of flight to the point of landing.

This indicates that the projectile is initially thrown at a height of 1.5 meters and a speed of 80.0 meters per second.

Since the bullet is launched horizontally, the initial vertical velocity component is zero. Just figure out how long it takes something to fall 1.5 meters from a seated position. The 80 m/s is only important if you want to know where it will land on the ground. It has no bearing on the situation. We might be led to the fundamental Newtonian equation:

hf = v₀t + (a/2)t² + h₀

Here, h stands for height, v for speed, and a for acceleration. It might be difficult to resolve this for t in some circumstances, however since

v₀ = 0, this one is easy.

0 = (-9.8/2)t² + 1.5

-1.5 = -4.9t²

-1.5/-4.9 = t²

0.55 s = t

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Fiber optic cable is available in 12 km lengths. How long will it take for a signal to travel that distance assuming that the speed of light in the cable is the same as in a vacuum?.

Answers

The Time it takes a signal to travel the length of the cable of 12 km if the speed of light in the cable and the vacuum are the same is  4×10⁻⁵ s.

What is time?

Time is the measured or measurable period during which an action, process, or condition exists or continues.

To calculate how long it will take a signal to travel a distance the same as the lenght of the cable, we use the formula below.

Formula:

t = d/v.......... Equation 1

Where:

t = Time it takes a signal to travel the length of the cabled = Length of the cablev = Speed of the signal/ speed of electromagnetic wave.

From the question,

Given:

d = 12 km = 12000 mv = 3×10⁸ m/s

Substitute these values into equation 1

t = 12000/(3×10⁸ m/s)t = 4×10⁻⁵ s

Hence, the time its takes a signal to travel the length of the cable is 4×10⁻⁵ s.

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what fluid property is responsible for the development of the velocity boundary layer? for what kinds of fluids will there be no velocity boundary layer in a pipe?

Answers

Fluid viscosity is the property of the fluid that is responsible for the development of the velocity boundary layer. Non-viscous fluids do  not exhibit the property of velocity boundary layer in a pipe.

What is fluid viscosity?

Thickness of a fluid is called its viscosity. In liquids, velocity boundary layer is formed due to viscosity.

Viscosity is also termed as the flow rate of a liquid. If a liquid has a high flow rate then its viscosity is low and vice versa.

The fluid viscosity can be measured by using viscometer. The formula to measure viscosity is F = μA. u/y

Here F is force,  μ is fluid viscosity, A is the area and u/y sheer deformation rate.

On the contrary, a non-viscous fluid is one that has less thickness and can flow easily.

For example, water is a non-viscous fluid.

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Please help me quickly

Answers

you need to show the problem
The total energy will Increase I think

A vector is 253 m long and points in a 55.8 degree direction. Find the y-component of the vector. Please help!! ​

Answers

Answer:

209.3 m

Explanation:

x component will be  253 cos 55.8

y component will be  253 sin 55.8 = 209.3 m

Someone is standing on a trampoline. They have a mass of 65kg and each of their feet a 25cm x 10cm, what is the pressure exerted by both on the trampoline?

Answers

The pressure exerted by both on the trampoline is 25,480 N/m².

What is the pressure exerted?

The pressure exerted by both on the trampoline is the force per unit area which is calculated as follows;

P = F/A

where;

F is the force applied by their weight A is the area of their feetP is the pressure exerted

Substitute the given parameters and solve for the pressure exerted.

P = (mg)/A

A = 0.25 m x 0.1 m

A = 0.025 m²

P = (65 x 9.8) / (0.025)

P = 25,480 N/m²

Thus, the pressure exerted at any given surface depends on the applied force and the area of the given surface.

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points :)




don't mind this just getting to 20 words :)

Answers

Answer:

20 20 20 20 25 points 20 20 20 25 points

Explanation:

HELP!

A box is sitting on a frictionless surface when a net force of 15 N is applied to the right. If the acceleration of the box is 0.33 m/s2 to the right, what is the mass of the box?

a
2.0 kg

b
5.0 kg

c
18 kg

d
45 kg

Answers

Answer:

F=m × a - answer is D

Explanation:

F=15N

m=m

a=0.33

15÷0.33=45.45...

18kg c is the right answrr

Why do the planets orbit the Sun?

A. The sun has enough mass to attract the planets

B. The sun has enough heat to attract the planets

C. The sun has enough velocity to attract the planets

D. The sun has enough energy to attract the planets

Answers

A. The sun has enough mass to attract the planets. is the correct statement for the given question.

What are planets?

A planet is a celestial body that revolves in an orbit around the Sun, planet has sufficient mass for self-gravity to overcome rigid body forces. It has space around its orbit to revolve around the sun. A gas Giant is a planet composed mainly of gas. Super-Earth is a rocky planet that is larger than Earth.

Neptune-like planets that are about the size of Neptune. A terrestrial is a rocky world that is outside our solar system. The basic reason the planets revolve around the Sun is the gravity of the Sun that keeps them in their orbits. As the Moon orbits the Earth because of the Earth's gravitational pull and the Earth orbits the Sun because of the Sun's gravitational pull.

So we can conclude that the planets orbit the Sun because the sun has enough mass to attract the planets.

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10. What is the solution of the equation
-9x + 4 = -8- 5x?
A x = -3
B x=
2/7
x = 1
℗ x = 3

Answers

The answer to your question is x=3

Answer:

x=3

-9x+4= -8-5x

+5x +5x

-4x+4= -8

-4 -4

-4x= -12

/-4. /-4

x=3

a toaster is designed to operate with a voltage of 120 v, and a clothes dryer is designed to operate with a voltage of 240 v. based solely on this information, which appliance uses more power?

Answers

Answers are impossible given the information provided.

P=VI, P=VI, where V is the voltage, I is the current, and P is the power, gives the power in an electric circuit.

We cannot draw any conclusions from the voltage measurement alone because power depends on both voltage and current. The information provided is therefore insufficient.

Answers are impossible given the information provided.

Describe voltage.

A lamp can be lit when charged electrons (current) are compelled through a conducting loop by the pressure of an electrical circuit's power source. In a nutshell, voltage equals pressure and is expressed in volts (V).

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A stone is projected upwards to an angle of 30° to the horizontal from the top of a tower of height 100m and it hits the
ground at a point Q. if the initial velocity of projection is 100m/s, calculate:
(0
Maximum height of the stone above the ground. (ii) Time it takes to reach this height (iii) Time of flight of the
stone. (iv) Horizontal distance from the foot of the tower to the point Q.

Answers

The correct answer are as follows

(i) 250 m is the maximum height

(ii) Time to reach the height is 5 s

(iii) Time of the flight is 10 s

(iv) Horizontal distance from the foot of the tower to point Q is 433 m

Given,  π°= stand as the angle= 30°

h= height= 100m

u= initial velocity= 100m/s

g= acceleration due to gravity= 10m/s²

(i) maximum height= h(max)= u²sin²π°/g

= 100²(sin30°)²/10

= 10000(0.25)/10

= 1000(0.25)

= 250m

height(max)= 250m

(ii)time it takes to reach the height= using π°/g

= 100sin30°/10

= 10 × 0.5

= 5

t= 5s

(iii)time of flight, T= 2t

T= 2(5)= 10

T= 10s

(iv)horizontal distance=H= u²cosπ°/2g

= 100²(cos 30°)/2(10)

= 10000(0.866)/20

= 500(0.866)

= 433

H ( distance)= 433m.

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