Answers
Answer:
[tex]\frac{dh}{dt}=-0.4125 m/s[/tex]
Explanation:
The very first thing we can do here is to draw a sketch of the situation the problem is presenting. (See attached picture)
As you may see in the picture, we can suppose the spotlight is directly located on the ground so the light of the spotlight together with the person and the wall make two similar triangles.
In this case we need to think about the dimensions of the triangle that will change over time. We will call them:
x= distance between the spotlight and the man.
h= height of the shadow.
So we can build a relation between the height and the length of each triangle:
[tex]\frac{h}{12}=\frac{2}{x}[/tex]
the distance between the spotlight and the wall is constant, so I can directly write the 12 in my equation and the height of the man is constant as well, so I can write the 2 directly into the equation.
Next, we can solve the equation for h (since we are interested in figuring out how fast the height of the shadow is decreasing) so we get:
[tex]h=\frac{24}{x}[/tex]
So next, we need to take the derivative of the equation, since the derivative of a position function will give us the velocity at which that position is changing.
First we rewrite the equation like this:
[tex]h=24x^{-1}[/tex]
and take the derivative:
[tex]dh=-24x^{-2}dx[/tex]
we can rewrite the derivative like this:
[tex]\frac{dh}{dt}=-\frac{24}{x^{2}} \frac{dx}{dt}[/tex]
where:
dh/dt is the velocity at which the height of the shadow is decreasing (that's why our equation has a negative sign in front of it).
dx/dt is the velocity at which the value of x is increasing. In other words, how fast the man is moving away from the spotlight.
So we can go ahead and substitute:
we wish to find the velocity at which the shadow's height is decreasing when the distance between the man and the building is 4m, so in this case, x=12-4=8m
[tex]\frac{dh}{dt}=-\frac{24}{8^{2}}(1.1 m/s)[/tex]
so we get:
[tex]\frac{dh}{dt}=-0.4125 m/s[/tex]
Related Questions
A 1000 kg car crashed into a barrier. The car changed speed from 30 m/s to 20 m/s in 0.2 seconds. What force did the barrier apply to stop the car?
Answers
Answer:
Force = -50000 Newton
Explanation:
Given the following data;
Initial velocity, u = 30 m/s
Final velocity, v = 20 m/s
Time = 0.2secs
Mass = 1000 kg
First of all, we have to solve for its acceleration.
Acceleration = (v - u)/t
Substituting into the equation, we have
Acceleration = 20 - 30)/0.2
Acceleration = -10/0.2
Acceleration = -50m/s²
To find the force;
Force = mass * acceleration
Force = 1000 * (-50)
Force = -50000 Newton. The value of the force is negative because it stopped the motion of the car.
Therefore, the barrier applied a force of -5,0000 Newtons to stop the car.
Answer: -50000
Explanation:
Marvin the Martian needs to get back home. Marvin is 321,770 m from his home on Mars. He decides the quickest way to get home is to use his canon to fire himself into flight. He aims the the canon at an angle of 25 degrees. When the canon is fired Marvin the Martian is launched into flight at an initial velocity of 1250 m/s. The question is will his plan work
Answers
Answer:
y = 14238 m. the height of the rocket is much less than this distance therefore the plan will not work.
Explanation:
Let's analyze this exercise, so that the Martian's plan works, the vertical height of the body must be zero when it is more than half of the way to the planet Mars, this is so that Mars attracts it and can arrive.
Let's calculate the maximum height of the launch
[tex]v_{y} ^2 = v_{oy}^2 - 2 g y[/tex]
at the highest point [tex]v_{y}[/tex] = 0
y = v_{oy}² / 2g
y = (v₀ sin θ)² / 2g
let's calculate
y = (1250 sin 25)² /2 9.8
y = 14238 m
In the exercise, indicate that the distance to Mars is h = 321770 m, half of this distance is
h / 2 = 160885 m
therefore the height of the rocket is much less than this distance therefore the plan will not work.
The height reached is low, so it is not necessary to take into account the variation of g with height
At what rate, in m/s2, does gravity cause objects to accelerate on Earth? Do not include units in your answer.
Answers
Answer:
9.8
Explanation:
I searched it up
..........
....
What is the purpose of the Bill of Rights?
to inspire the governments of other nations
to limit the rights of individual citizens
to explain the procedure for amending the Constitution
to guarantee freedoms that belong to every citizen
Answers
Answer:
i think it is To limit the rights of individual citizens
Explanation:
The heat vaporization for methyl alcohol is 1100 kj/kg. It is 2257 KJ/Kg for water. Thus means that______________.
A) these are the amounts of energy to change temperature 1 degree C. required for these substances
B) Methyl alcohol requires less than half as much energy per kg to evaporate than water doe
C) water will get twice as ot as methyl alcohol during vaporization.
d) when alcohol and water evaporate they release 2,2 kj and 2257 kj of energy for every kg respectivly
Please hurry! I'm being timed!
Answers
Answer: B) Methyl alcohol requires less than half as much energy per kg to evaporate than water does
Explanation:
Latent heat of vaporization is the amount of heat required to convert 1 kilo gram of liquid into its vapor state without change in its temperature.
Heat of vaporization is more for water than for methyl alcohol which means more heat is required to convert from liquid to vapour form.
As the Heat of vaporization for methyl alcohol (1100) is almost half as that of Heat of vaporization for water (2257) , it means Methyl alcohol requires less than half as much energy per kg to evaporate than water does.
Will give brainliest if correct
Please help
Answers
Answer:
85.45
Divide 4,700/55
So C.
Answer:
C.85
Explanation:
Use the equation:
v= fλ ( v=wave speed, f= frequency, λ= wavelength)
4700= 55×λ
λ=4700÷55 =85.45 =85(approximately)
A boy climbs 12.0m up an apple tree. He picks an apple and throws it horizontally with a velocity of 3.0 m/s. How far forward does the ball go before it hits the ground
Answers
Answer:
4.692m
Explanation:
The distance that this boy climbed = 12.0m
The velocity = 3.0m/s
We are to find how far forward this apple goes before it hits the ground.
We have y = 1/2gt²
X = v*t
T = 1.564 seconds
X = 3x1.564
X = 4.692m
Therefore the ball goes a distance of 4.692m forward before it then hits the ground.
A block slides along a frictionless surface and onto a slab with a rough surface. The slab has mass of 4 kg and the block has mass of 2 kg. What is the friction force on the small block at t = 1 second?
Answers
Answer: the friction force on the small block at t equals 1 second is 2N
Explanation:
Given the data in the question;
from the slope in the graph provided, we will get the acceleration of the slab
At t = 1 seconds
Slope = acceleration = ( 1 - 0) / ( 2 - 0 ) = 1/2 = 0.5 m/s²
Force = ma = 4 × 0.5 = 2 N
so by Newton's third law
Force on block will be same which is 2N
Therefore the friction force on the small block at t equals 1 second is 2N
⚠️Please Help Me! I Need It Now!⚠️
Answers
Answer:
A. They are moving at 60 mph
Explanation:
When looking at the car on the track pass by, the people inside appear to be moving at the same speed as the car. So if the car is going 60 mph, the people instead will appear as though they are moving at 60 mph as well.
a projectile is shot upward from the surface of the earth with an initial velocity of 384 ft/s. What is its velocity after 5 seconds
Answers
Answer:
335 ft/s
Explanation:
In this question, we have a very important factor missing. The equation of the projectile. So, in simplifying the question I'm going to assume an equation which you can correct thereafter
s(t) = -4.9t² + v(0)t + s0
From the question, we're told that v(0) = 384 ft/s, so if we apply that, we have
s(t) = -4.9t² + 384t + s0, where s0 = 0
On differentiating the equation, we have
s(t) = v(t) = -4.9(2t) + 384(1)
v(t) = -9.8t + 384
Now, at time t = 5 seconds, the velocity v =
v(t) = -9.8(5) + 384
v(t) = -49 + 384
v(t) = 335 ft/s
Therefore, the velocity of the projectile after 5 seconds is 335 ft/s. Please leave a like if it helped you.
A 2kg object is tied to the end of a cord and whirled in a horizontal circle of radius 2 m. If the body makes three complete revolutions every second,
what is its linear speed?
And what is its centripetal acceleration?
Answers
Answer:
a) 37.70 m/s
b)710.6 m/s²
Explanation:
Given that ;
Mass of object = 2 kg
Radius of the motion = 2m
Frequency of motion = 3 rev/s
The formula to apply is;
v= 2πrf where v is linear speed
v = 2×π×2×3 =12π = 37.70 m/s
Centripetal acceleration is given as;
a= 4×π²×r×f²
a= 4×π²×2×3²
a=710.6 m/s²
An 85 kg man stands in a very strong wind moving at 15 m/s at torso height. As you know, he will need to lean in to the wind, and we can model the situation to see why. Assume that the man has a mass of 85 kg, with a center of gravity 1.0 m above the ground. The action of the wind on his torso, which we approximate as a cylinder 50 cm wide and 90 cm long centered 1.2 m above the ground, produces a force that tries to tip him over backward. To keep from falling over, he must lean forward.
Required:
a. What is the magnitude of the torque provided by the wind force? Take the pivot point at his feet. Assume that he is standing vertically.
b. At what angle to the vertical must the man lean to provide a gravitational torque that is equal to this torque due to the wind force?
Answers
Answer:
a) [tex]T= 72.9 Nm[/tex]
b) [tex]\Theta = 5 \textdegree[/tex]
Explanation:
From the question we are told that
Mass 85kg
Speed 15m/s
Center of gravity 1.0m
Cylinder 50 cm wide and 90 cm long centered 1.2 m above the ground
a)Generally equation for force is given by
[tex]F = 0.5 p A v^2[/tex]
Mathematically solving for force exacted
[tex]F = 0.5*1.2*0.9*0.5*15^2[/tex]
[tex]F= 60.75 N[/tex]
Mathematically solving for torque
Torque,
[tex]T = r * F[/tex]
[tex]T=1.2*60.75[/tex]
[tex]T= 72.9 Nm[/tex]
b)Generally in solving for [tex]\theta[/tex]
[tex]Tan\theta = Torque/(Mass * Gravity)[/tex]
[tex]Tan\theta = (72.9)/(85 * 9.8)[/tex]
[tex]\Theta = 5 \textdegree[/tex]
why does the force of air resistance affect the motion of a person traveling at high speed more than a person walking across the room?
Answers
Answer:
yes .
Explanation:
...
;-; :) have a good day
Answer:
because on air the speed is high compared to walking
Helppp!!
Research indicates that teenagers tend to become impaired by alcohol
adults.
A. faster than
B. slower than
C. at the same rate as
Answers
Answer:
A faster because teens what to drink it more when. they see there parents do it
Research indicates that teenagers have a faster tendency compared to adults in these case.
What are the process to encourage good behavior in pre-teens and teenagers?Good behavior in pre-teens and teenagers starts with positive communication and warm relationships. This lays the foundation for guiding your child’s behavior in a positive way.
Here are some practical tips for putting this positive approach into action.
Active listening entails paying close attention to your child's words and body language while they are being said. This enables you to pay attention to your child's feelings and thoughts. Additionally, it demonstrates to your child your concern and interest in them.Clear expectations concerning behaviour are outlined in family rules. Include every member of the family in the rule-setting talks, if you can. Maintaining good rules is important. For instance, you might say, "We treat each other with respect," rather than, "Don't be disrespectful."Find more about teenagers, refer the link:
https://brainly.com/question/3235532
#SPJ2
what is true about ocean water that is more dense?
1. It is generally warmer water.
2. It sinks to the bottom.
3. It has a lower salinity than less dense water.
4. It rises to the surface.
Answers
Answer:
Ocean water is more dense because of the salt in it. ... Temperature has a greater effect on the density of water than salinity does. So a layer of water with higher salinity can actual float on top of water with lower salinity if the layer with higher salinity is quite a bit warmer than the lower salinity layer.
An ostrich with a mass of 141 kg is running to the right with a velocity of 13m/s. Find the momentum of the ostrich. Answer in units of Kg.m/s
Answers
Answer:
1833 kg.m/sExplanation:
The momentum of an object can be found by using the formula
momentum = mass × velocity
From the question we have
momentum = 141 × 13
We have the final answer as
1833 kg.m/sHope this helps you
what medical uses does radiation have?
Answers
Answer:
Radiation is used in monitoring the response of tumors to treatment and in distinguishing malignant tumors from benign ones. Bone and liver scans can detect cancers that have spread to these organs. Half of all people with cancer are treated with radiation, and the number of those who have been cured continues to rise.
Explanation:
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Find the applied voltage of a telephone circuit that draws 0.017A through a resistance Of 5,000 ohms
Answers
A projectile is fired with a velocity of 8 m/s at an angle of 65º. What is the
vertical component of the velocity?
A. 6.5 m/s
B. 3.4 m/s
C. 10.2 m/s
D. 7.2 m/s
Answers
Answer:
i think its D
Explanation:
Four students were loading boxes of food collected during a food drive. The force that each student exerted while lifting and the distance each box was lifted are listed in the table.
A 3-column table with 4 rows. The first column labeled student has entries Chet, Mika, Sara, Bill. The second column labeled Force (Newtons) has entries 50, 40, 30, 60. The third column labeled Distance (meters) has entries 1.0, 2.0, 1.5, 0.5.
Which lists the students in order from the greatest amount of work done to the least? (Work: W = Fd)
Answers
Answer:
The correct answer is B. Mika, Chet, Sara, Bill
Explanation:
Look at the picture
hope this helps :)
The list, that the students in order from the greatest amount of work done to the least, is: Mika, Chet, Sara, Bill.
What is work?We can state that Work is the product of the component of the force acting in the displacement's direction and its magnitude.
The joule (J), a unit of work used in the International System of Units (SI), is defined as the amount of work required to move an item one meter in the direction of a force of one newton.
Work done by Mika = 50 × 1.0 Joule = 50 Joule
Work done by Chet = 40 × 2.0 Joule = 80 Joule
Work done by Sara = 30 × 1.5 Joule = 45 Joule
Work done by Bill = 60 × 0.5 Joule = 30 Joule
So, The list, that the students in order from the greatest amount of work done to the least, is: Mika, Chet, Sara, Bill.
Learn more about work here:
https://brainly.com/question/18094932
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let's say you hypothetically ran over someone with your car, and they are now under your car in between the front wheels and the back wheels, right, and they're stuck as in can't breathe type stuck, right, do you keep driving so they can breathe or do you let them chill under your car?
just curious...
Answers
question: is this actually hypothetical?
Explanation:
also just leave the car there go get some McDonald's or sum and come back and if they're still breathing then go ahead and move the car .
Answer:
the same thing the last guy said
11. Which element in Figure 15.17 is likely to be a the best conductor of electricity ?
Answers
Answer:
first where is figure...
silver the is best conducter of electricity.
A volleyball experiences 494 Ns of impulse over a time period of 7 seconds. What was the magnitude of the force that acted on the volleyball during this time period?
Answers
Answer:
70.6N
Explanation:
Given parameters:
Impulse = 494Ns
Time = 7s
Unknown:
Force applied = ?
Solution:
To solve this problem, we use the formula of impulse;
Impulse = Force x time
Now insert the parameters and solve;
494 = Force x 7
Force = [tex]\frac{494}{7}[/tex]
Force = 70.6N
The masses of the two moons are determined to be 2M2M for Moon AA and MM for Moon BB . It is observed that the distance between Moon BB and the planet is two times that of the distance between Moon AA and the planet. How does force exerted from the planet on Moon AA compare to the force exerted from the planet on Moon BB
Answers
Answer:
F_A = 8 F_B
Explanation:
The force exerted by the planet on each moon is given by the law of universal gravitation
F = [tex]G \frac{m M}{r^{2} }[/tex]
where M is the mass of the planet, m the mass of the moon and r the distance between its centers
let's apply this equation to our case
Moon A
the distance between the planet and the moon A is r and the mass of the moon is 2m
F_A = G \frac{2m M}{r^{2} }
Moon B
F_B = G \frac{m M}{(2r)^{2} }
F_B = G \frac{m M}{4 r^{2} }
the relationship between these forces is
F_B / F_A = [tex]\frac{1}{2 \ 4 }[/tex] = 1/8
F_A = 8 F_B
Answer:
F_A = 8 F_B
Explanation:
The force exerted by the planet on each moon is given by the law of universal gravitation
F =
where M is the mass of the planet, m the mass of the moon and r the distance between its centers
let's apply this equation to our case
Moon A
the distance between the planet and the moon A is r and the mass of the moon is 2m
F_A = G \frac{2m M}{r^{2} }
Moon B
F_B = G \frac{m M}{(2r)^{2} }
F_B = G \frac{m M}{4 r^{2} }
the relationship between these forces is
F_B / F_A = = 1/8
F_A = 8 F_B
23. What mass of water will give up 240 calories
when its temperature drops from 80°C to 68°C?
Answers
Answer:
20g
Explanation:
Given parameters:
Quantity of heat = 240calories
Initial temperature = 80°C
Final temperature = 68°C
Unknown:
Mass of water = ?
Solution;
To solve this problem, we use the expression:
Q = m c (t₂ - t₁)
Q is the quantity of heat
m is the mass
c is the specific heat = 1 cal/g°C
t₂ is the final temperature
t₁ is the initial temperature
Insert the parameters and solve;
Change in temperature is an absolute value
240 = m x 1 x (68 - 80)
m = 20g
A slide projector projects images on a screen. a) If the slide is 15.5 cm from the lens and the lens has a focal length of 15 cm, how far away is the screen
Answers
Answer:
[tex]d_{i}=465 cm=4.65 m[/tex]
Explanation:
Using the thin lens equation, we have:
[tex]\frac{1}{f}=\frac{1}{d_{o}}+\frac{1}{d_{i}}[/tex]
Where:
f is the focal length
d(o) is the distance of the object
d(i) is the distance of the image
[tex]\frac{1}{15}=\frac{1}{15.5}+\frac{1}{d_{i}}[/tex]
[tex]\frac{1}{15}-\frac{1}{15.5}=\frac{1}{d_{i}}[/tex]
[tex]d_{i}=465 cm=4.65 m[/tex]
Therefore, the screen is at 465 cm.
I hope it helps you!
A construction laborer holds a 20 kg sheet of wallboard 3 m above the floor for 4 seconds. During these 4 seconds how much power was expended on the wallboard
Answers
Answer:
zero
Explanation:
no distance has moved while holding the sheet...so no distance means no workdone..no workdone means no power...
Caca box like fish no earnings play like caca
400 points in arena youa have none thats Why I wonder
Answers
Answer:
I actually have 20000 arena points thank you very much
Answer: Caca means in French lol.
There are 25 elements found in living things. How many of these elements are found in some organisms but not all?
1
6
19
25
Answers
Answer: 6
Explanation:
Of those 25 elements found in living things, 6 of them can be found in all of them. These 6 are very integral to life as when they combine, they make up cells, tissues and other body components.
These elements are: Carbon, Oxygen, Nitrogen, Hydrogen, Phosphorus and Sulfur. Their combinations can either create organic or inorganic compounds.
Answer:
19
Explanation:
i got 19... not sure if 6 is correct
What type of telescope did Galileo use to observe Jupiter?
reflector telescope
refractor telescope
radio telescope
latter telescope
Answers
Answer:
a refractor telescope
Explanation:
Answer:
a. refractor telescope
