.Finding Height and Speed of Stone Impacting a Cliff

In summary, the stone is projected at a cliff of height h with an initial speed of 46.0 m/s directed 60.0° above the horizontal. The stone strikes the cliff, 5.10 s after launching.
  • #1
iamkristing
33
0
1.a stone is projected at a cliff of height h with an initial speed of 46.0 m/s directed 60.0° above the horizontal. The stone strikes the cliff, 5.10 s after launching.

(a) Find the height, h, of the cliff.


(b) Find the speed of the stone just before impact at A.


(c) Find the maximum height H reached above the ground.



Homework Equations





The Attempt at a Solution



i was able to answer a and b. c was giving me trouble. i divided the horizontal and vertical velocities and tried to solve from there but could not come up with an answer
 
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  • #2
You know the height of the cliff, correct?

Now, can you find the maximum height the ball reaches above it's starting point (top of the cliff)? If you can, you should be able to answer c.

Try drawing a diagram if you do not see how this helps you obtain the answer.
 
  • #3
Sorry I should clarify the question.

The stone is launched from 0 m and lands on a cliff with a height of 75.5 m. I'm looking for the maximum height of the stone...
 
  • #4
use ...
max ht=[vo^2sin^2 theta]/2g

in plave of vo put the 46 m/s you have.
 
  • #5
iamkristing said:
Sorry I should clarify the question.

The stone is launched from 0 m and lands on a cliff with a height of 75.5 m. I'm looking for the maximum height of the stone...

Ahh ok that makes it clearer. I must have read the problem incorrectly. I read "projected off the cliff, instead of "at the cliff."

HINT: To find the maximum height work with the y direction information.

What is the speed in the y direction at the highest point?

What is the initial speed in the y direction?

What about the acceleration in the y direction?

Can you use this information to find the change in position, i.e. the height of the highest point?
 

FAQ: .Finding Height and Speed of Stone Impacting a Cliff

1) How do you calculate the height and speed of a stone impacting a cliff?

The height and speed of a stone impacting a cliff can be calculated using the equations of motion. The height can be found using the equation h = u2sin2(θ)/2g, where u is the initial velocity of the stone, θ is the angle at which the stone is thrown, and g is the acceleration due to gravity. The speed can be calculated using the equation v = ucos(θ), where v is the final velocity of the stone.

2) What factors affect the height and speed of a stone impacting a cliff?

The height and speed of a stone impacting a cliff are affected by various factors such as the initial velocity of the stone, the angle at which it is thrown, the acceleration due to gravity, and the air resistance. The height and speed will also vary depending on the height and slope of the cliff.

3) Can you use the same equations to calculate the height and speed of a stone thrown horizontally?

Yes, the same equations can be used to calculate the height and speed of a stone thrown horizontally. In this case, the angle θ would be equal to 0, and the equations will reduce to h = u2/2g and v = u.

4) How does air resistance affect the height and speed of a stone impacting a cliff?

Air resistance will decrease the speed and height of a stone impacting a cliff. This is because air resistance acts as a force opposing the motion of the stone, reducing its velocity and therefore its impact force on the cliff.

5) What are some real-world applications of calculating the height and speed of a stone impacting a cliff?

Calculating the height and speed of a stone impacting a cliff can be useful in various real-world situations. It can be used in sports such as rock climbing and cliff jumping to ensure the safety of the participants. It can also be used in engineering to determine the impact force of falling objects on structures, and in forensic science to analyze the trajectory of thrown or dropped objects at a crime scene.

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