Sandra shot a rocket so that it moved with an initial velocity of 9.81 m/s straight upward. The rocket leaves and returns to ground level. What is the total time the rocket was in the air before it strikes the ground? (Ignore air resistance.

Newton’s laws explain why scientists could expect this to happen , The mass of the rocket decreases as fuel is burned, so the acceleration increases, therefore the correct answer is option B.

Newton's Second Law states that The resultant force acting on an object is proportional to the rate of change of momentum. The mathematical expression for Newton's second law is as follows

As given in the problem Scientists launch a rocket, and they monitor its acceleration and the force exerted by its engines. As the rocket gets higher, the monitors show that the acceleration of the rocket is increasing but the force exerted stays the same.

Newton's laws clarify why scientists may anticipate this to occur. The right response is option B because as fuel is burnt, the rocket's mass reduces, and its acceleration rises.

Learn more about Newton's second law here,refer to the link given below ;

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Answer:

Average speed (s) = total distance/total elapsed tiime

Explanation:

To calculate the average speed of an object, you must know the total distance an object travels and the total elapsed time of its whole journey.

Answer:

To find the average speed of an object, divide the total distance covered by the object by the total time it takes the object to cover such distance.

average speed= total distance covered/total time

Answer:

The batteries

Explanation:

Answer:

a)  x = 5923.6 m ,  b) directly above the bomb ahead of the bomb,

c)  θ = 65.3º

Explanation:

This is a projectile launching exercise

a) As the package is released from the plane at its same speed, vox 0 251 m / s, they indicate that the plane flies horizontally, therefore the initial vertical speed is zero, let's calculate the time of arrival to the ground

       y = y₀ + [tex]v_{oy}[/tex] t - ½ g t²

to the ground y = 0

       0 = y₀ + 0 - ½ g t²

       t = √ (2y₀ / g)

      t = √ (2 2730 / 9.8)

      t = 23.60 s

the horizontal distance traveled is

      x = v₀ₓ t

      x = 251 23.6

      x = 5923.6 m

b) since there is no acceleration on the x-axis and it is indicated that the air resistance is zero in part it must be just below the plane

directly above the bomb ahead of the bomb

c) for this part we can use trigonometry

since the angle with respect to the vertical is requested, the opposite leg is the horizontal distance

           tan θ = x / y

           θ = tan⁻¹ (x / y)

           θ = tan⁻¹ (5923.6 / 2730)

           θ = 65.3º

Solution:

1. millimeter, centimeter

 1 centimeter = 10 millimeter

 So, centimeter is the larger unit here.

2. kilogram, megagram

    1 megagram = 1000 kilogram

   So, megagram is the larger unit here.

3. microsecond, millisecond

    1 millisecond = 1000 microsecond

   So, millisecond is the larger unit here.

4.dL, mL

  1 dL = 100 mL

So, dL is the larger unit here.  

5.mg, kg

  1 mg = 0.000001 kg

 So, kg is the larger unit here.

6. Mm,mm

   1 mm = 1 mm

  Both are same

7. S, cs

   1 second = 100 centisecond

So, S is the larger unit.  

8. M, mm

   1 M  = 1000 mm

So, M is the larger unit here.  

9. U s, ks

   Us is larger.

Answer:

The required  total area is 1.48 m²

Explanation:

Given that,

Latitude = 44+° N

New Mexico,

Latitude= 35+° N

Heat capacity = 4200 J/Kg°C

Temperature = 60°C

Let us assume the input temperature 22°C

Estimate volume of water 100 ltr for 4 person.

We need to calculate the heat

Using formula of heat

[tex]H=mc_{p}\Delta T[/tex]

[tex]H=mc_{p}(T_{f}-T_{i})[/tex]

Put the value into the formula

[tex]H=100\times4200\times(60-22)[/tex]

[tex]H=15960\ KJ[/tex]...(I)

Let solar radiation for 6 hours/day.

We need to calculate the total energy per unit area

Using formula of energy

[tex]E=1000\times6\times3600\ J/m^2[/tex]

[tex]E=21600\ KJ/m^2[/tex]

Let the efficiency of collector is 50 %

Then,  the total energy per unit area will be

[tex]E=21600\times\dfrac{50}{100}[/tex]

[tex]E=10800\ KJ/m^2[/tex]....(II)

We need to calculate the required total area

Using equation (I) and (II)

[tex]A=\dfrac{H}{E}[/tex]

Where, H = heat

E = total energy

Put the value into the formula

[tex]A=\dfrac{15960}{10800}[/tex]

[tex]A=1.48\ m^2[/tex]

Hence, The required  total area is 1.48 m²

Answer:

yes SI units are used for scientific works

Explanation:

because they are standard units and can be used by anyone easly

Answer:

true

Explanation:

Answer:

[tex]a[/tex] has units of distance

[tex]b[/tex]  has units of distance over time

[tex]c[/tex]  has units of distance over [tex]time^2[/tex]

[tex]d[/tex] has units of distance over [tex]time^3[/tex]

Explanation:

Since the expression for the distance is:

[tex]x = a+b\,t+c\,t^2+d\,t^3[/tex]

then:

[tex]a[/tex] has units of distance

[tex]b[/tex]  has units of distance over time

[tex]c[/tex]  has units of distance over [tex]time^2[/tex]

[tex]d[/tex] has units of distance over [tex]time^3[/tex]

because we are supposed to be able to add all of the terms and get a distance.  So the products on each term that contains factors of time (t) should be cancelling those time units with units in the denominator of the multiplicative constant s that accompany them.

Answer:

the hot bulb will have high resistance to the flow of current. While the cold bulb will have a low resistance to the flow of current.

Explanation:

A conductor that does not obey Ohm's law is described as non - ohmic. An example is a filament lamp. It glows as the current passes through it.

How does the resistance of the light bulbs differ when the bulbs are cold and when the bulbs are hot ?

The resistance of the light bulbs increase gradually as its temperature is increased.

So, the hot bulb will have high resistance to the flow of current. While the cold bulb will have a low resistance to the flow of current.

Because the resistance of an impure metal wire is greater than the resistance of a pure metal wire of the same dimension.

The question is missing some parts. Here is the complete question.

An ideal gas is contained in a vessel at 300K. The temperature of the gas is then increased to 900K.

(i) By what factor does the average kinetic energy of the molecules change, (a) a factor of 9, (b) a factor of 3, (c) a factor of [tex]\sqrt{3}[/tex], (d) a factor of 1, or (e) a factor of [tex]\frac{1}{3}[/tex]?

Using the same choices in part (i), by what factor does each of the following change: (ii) the rms molecular speed of the molecules, (iii) the average momentum change that one molecule undergoes in a colision with one particular wall, (iv) the rate of collisions of molecules with walls, and (v) the pressure of the gas.

Answer: (i) (b) a factor of 3;

              (ii) (c) a factor of [tex]\sqrt{3}[/tex];

              (iii) (c) a factor of [tex]\sqrt{3}[/tex];

             (iv) (c) a factor of [tex]\sqrt{3}[/tex];

              (v) (e) a factor of 3;

Explanation: (i) Kinetic energy for ideal gas is calculated as:

[tex]KE=\frac{3}{2}nRT[/tex]

where

n is mols

R is constant of gas

T is temperature in Kelvin

As you can see, kinetic energy and temperature are directly proportional: when tem perature increases, so does energy.

So, as temperature of an ideal gas increased 3 times, kinetic energy will increase 3 times.

For temperature and energy, the factor of change is 3.

(ii) Rms is root mean square velocity and is defined as

[tex]V_{rms}=\sqrt{\frac{3k_{B}T}{m} }[/tex]

Calculating velocity for each temperature:

For 300K:

[tex]V_{rms1}=\sqrt{\frac{3k_{B}300}{m} }[/tex]

[tex]V_{rms1}=30\sqrt{\frac{k_{B}}{m} }[/tex]

For 900K:

[tex]V_{rms2}=\sqrt{\frac{3k_{B}900}{m} }[/tex]

[tex]V_{rms2}=30\sqrt{3}\sqrt{\frac{k_{B}}{m} }[/tex]

Comparing both veolcities:

[tex]\frac{V_{rms2}}{V_{rms1}}= (30\sqrt{3}\sqrt{\frac{k_{B}}{m} }) .\frac{1}{30} \sqrt{\frac{m}{k_{B}} }[/tex]

[tex]\frac{V_{rms2}}{V_{rms1}}=\sqrt{3}[/tex]

For rms, factor of change is [tex]\sqrt{3}[/tex]

(iii) Average momentum change of molecule depends upon velocity:

q = m.v

Since velocity has a factor of [tex]\sqrt{3}[/tex] and velocity and momentum are proportional, average momentum change increase by a factor of

(iv) Collisions increase with increase in velocity, which increases with increase of temperature. So, rate of collisions also increase by a factor of [tex]\sqrt{3}[/tex].

(v) According to the Pressure-Temperature Law, also known as Gay-Lussac's Law, when the volume of an ideal gas is kept constant, pressure and temperature are directly proportional. So, when temperature increases by a factor of 3, Pressure also increases by a factor of 3.

Answer: 490

Explanation:

Answer:

i think its A

Explanation:

Answer:

Total energy =kinetic energy +potential energy.

Answer:

Kinetic Energy + Potential Energy = total energy

Explanation:

The conservation of mechanical energy can be written as “KE + PE = const”. Though energy cannot be created nor destroyed in an isolated system, it can be internally converted to any other form of energy.

Answer:

total distance travelled

Explanation:

Answer:

The value is  [tex]KE = 9 J[/tex]

Explanation:

From the question we are told that

      The mass is  [tex]m = 0.5 \ kg[/tex]

     The velocity is  [tex]v = 6 \ m/s[/tex]

Generally the kinetic energy is mathematically represented as

        [tex]KE = \frac{ 1}{2} * m*v^2[/tex]

=>     [tex]KE = \frac{ 1}{2} * 0.5*6^2[/tex]

=>     [tex]KE = 9 J[/tex]

Answer:

Mass

Explanation:

kinetic energy (KE) is equal to half of an object's mass (1/2*m) multiplied by the velocity (speed) squared.

Answer:

A)6.6×10^22atoms of Pt in the cube

B)1.4×10^-8m

Explanation:

(a) Calculate the number of Pt atoms in the cube.

an edge length of platinum (Pt) = 1.0 cm.

Then Volume= 1.0 cm×1.0 cm×1.0 cm=1cm^3

Then we have volume of the cube as 1cm^3

Given:

The density Pt = 21.45 g/cm3

the mass of a single Pt atom =3.240 x 10^-22 g

Then with 1atom of the platinum element, we can calculate the number of Pt atoms in the cube as

Density of pt/mass of a single Pt atom

=(21.45 /=3.240 x 10^-22)

=6.6×10^22atoms of Pt in the cube

B)Volume of cube V=4/3πr^3

V= 4/3 ×π×r^3

V= 4.19067r^3

r^3= V/4.19067

But volume is not total volume but just 74% of it, then With 74% of the space inside the cube is taken up by Pt atoms, then we need to find 74% of volume of the cube which is 1cm^3

74/100 ×1= 0.74cm^3

Then our new volume V is 0.74cm^3

r^3=0.74/4.19067×6.620 x 10^22

r^3=2.6674×10^-24

r= 3√2.6674×10^-24

r=1.4×10^-8m

Answer:

The car furthest from the finish line: Car III (Choice C).

Explanation:

It's asking for lowest average speed throughout the entire race. Therefore, whoever is last technically has the lowest average speed.

Car III is far behind Car I and Car II so Choice A and B aren't correct. Choice D is incorrect since the three cars aren't in the same position. Choice E is incorrect because there is enough information to see that Choice C has the lowest average speed.

Answer:

Explanation:

When an object experiences acceleration to the left, the net force acting on this object will also be to the left.

From Newton's second law of motion, the acceleration of the object is given as;

a = ∑F / m

a = -F / m

The negative value of "a" indicates acceleration to the left

where;

∑F is the net force on the object

m is the mass of the object

At a constant force, F = ma ⇒ m₁a₁ = m₂a₂

If the mass of the object was doubled, m₂ = 2m₁

a₂ = (m₁a₁) / (m₂)

a₂ = (m₁a₁) / (2m₁)

a₂ = ¹/₂(a₁)

Therefore, the following can be deduced from the acceleration of this object;

Answer:

h2o and o2

Explanation:

Answer:

Vf = 22.62 [m/s] in 2 seconds.

Explanation:

In order to solve this problem we must use the following kinematics equation

[tex]v_{f} = v_{i} + (g*t)[/tex]

where:

Vf = final velocity [m/s]

Vi = initial velocity = 3 [m/s]

g = gravity acceleration = 9.81 [m/s^2]

t = time = 2 [s]

Vf = 3 + (9.81*2)

Vf = 22.62 [m/s]

Answer:

She must throw it in the opposite direction away from herself and the ship at a velocity of -8.33 m/s.

Explanation:

She must throw it in the opposite direction away from herself and the ship. To find the velocity with which she throws it, we consider the law of conservation of momentum.

Since initial momentum = final momentum and the initial momentum of the astronaut and wrench = 0

0 = final momentum

0 = mv + MV where m = mass of wrench = 1.0 kg, v = velocity of wrench, M = mass of astronaut + suit = 100 kg and V = velocity of astronaut.

So. mv = -MV

v = -MV/m

Now, if the astronaut is supposed to cover a distance of 100 m from the space ship in 20 minutes, her velocity should be, V = distance/time = 100 m/ 20 min = 100 m/(20 × 60 s)  = 100 m/1200 = 0.0833 m/s

So v = -MV/m

= -100 kg × 0.0833 m/s ÷ 1.0 kg

= -8.33 m/s

She must throw the wrench in the opposite direction away from herself and the ship at a velocity of -8.33 m/s.

Divide the change in speed by the given time:

a = (9.38 m/s - 5.25 m/s) / (4.27 s) ≈ 0.967 m/s²

Answer:

The acceleration is  6 [tex]\frac{m}{s^2}[/tex]

Explanation:

Use Newton's second law to solve the problem:

[tex]Force = mass\,\,*\,\,acceleration\\3\,N = 0.5\,\,kg\,*\,a\\a = \frac{3}{0.5} \frac{m}{s^2} \\a=6\,\,\frac{m}{s^2}[/tex]

the acceleration of the cart given its mass and force exerted is 6m/s².

Given the data in the question;

Mass of lab cart; [tex]m = 0.5kg[/tex]

Force applied; [tex]F = 3N[/tex]

Acceleration of cart; [tex]a = \ ?[/tex]

To determine the acceleration of the cart, we use the expression from Newton's second law of Motion:

[tex]F = m* a[/tex]

Where F is force exerted, m is mass and a is acceleration

We substitute our given values into the equation

[tex]3N = 0.5kg \ * \ a\\\\3kgm/s^2 = 0.5kg\ *\ a\\\\a = \frac{3kgm/s^2}{0.5kg} \\\\a = 6m/s^2[/tex]

Therefore, the acceleration of the cart given its mass and force exerted is 6m/s².

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Answer:

a. 50.9 mΩ b. 9.32 × 10¹⁸ electrons/s c. 4.55 × 10⁵ A/m² d. i. resistance and current density  ii. They would decrease.

Explanation:

a. The resistance of the copper wire is given by

R = ρl/A where ρ = resistivity of copper wire = 1.68 × 10⁻⁸ Ωm, l = length of copper wire = 10 m and A = cross-sectional area of coper wire = πd²/4 where d = diameter of copper wire = 2.05 mm = 2.05 × 10⁻³ m

A =  πd²/4  

= π(2.05 × 10⁻³ m)²/4

= 13.2025/4  × 10⁻⁶ m²

= 3.3 × 10⁻⁶ m².

So R = ρl/A

=  1.68 × 10⁻⁸ Ωm × 10 m/3.3 × 10⁻⁶ m²

= 0.0509 Ω

= 50.9 mΩ

b. Since a current of 1.5 A flows through the wire, it means that 1.5 C/s, that is 1.5 Coulombs of charge flows through it per second.

Since 1 electron = 1.609 × 10⁻¹⁹ C, the number of electrons in 1.5 A is 1.5 C/s ÷ 1.609 × 10⁻¹⁹ C per electron = 1.5/1.609 × 10⁻¹⁹ C = 9.32 × 10¹⁸ electrons/s

c. The current density J = I/A where I = current = 1.5 A and A = cross-sectional area of copper wire = 3.3 × 10⁻⁶ m²

J = 1.5 A/3.3 × 10⁻⁶ m²

= 4.55 × 10⁵ A/m²

d. i. If the diameter were twice the initial diameter, d' = 2d, then the resistance and current density would change since they are dependent of the cross-sectional area of the wire which is then dependent on the diameter of the wire.

ii. If the diameter were twice the initial diameter, d' = 2d, then since the cross-sectional area A' = πd'²/4 = π(2d)²/4 = 4πd²/4 = 4A. So, the cross-sectional area increases by a factor of four.

The new resistance R' =  ρl/4A = R/4

The new current density J' = I/4A = J/4.

So the resistance and current density would decrease.

I'll assume you mean the hill is 150 m along its slope, since that's the direction the ball rolls.

The distance x it rolls after time t is

x = (2.5 m/s) t + 1/2 (6.3 m/s²) t²

Set x = 150 m and solve for t :

150 m = (2.5 m/s) t + 1/2 (6.3 m/s²) t²

(3.15 m/s²) t² + (2.5 m/s) t - 150 m = 0

t = 1/2 [(-2.5 m/s) + √((2.5 m/s)² - 4 * (3.15 m/s²) * (-150 m))]

(Use the quadratic formula, and take the positive root)

t ≈ 6.52 s