Find the Height of Ball and Stone at Intersection | Vertical Freefall Problem

In summary, the conversation discusses the scenario of a ball and stone being thrown vertically upward from the same initial height with different initial speeds. The acceleration of gravity is given as 9.8 m/s^2. The question asks for the distance above the release point where the ball and stone will pass each other, and the solution involves solving for the time and then plugging it into one of the height equations to find the height at that time.
  • #1
AraProdieur
27
0
A ball is thrown vertically upward with an initial speed of 15 m/s. Then, 0.92 s later, a stone is thrown straight up ( from the same initial height as the ball) with an initial speed of 27 m/s. The acceleration of gravity is 9.8 m/s^2.
How far above the release point will the ball and stone pass each other? Answer in units of m.

So far, I have written down this equation 15( t + 0.92) - 4.9(t + 0.92)^2= 27t- 4.9t^2
And when I simplify everything, I get a t= .4593

Now, I don't know if that is even remotely correct, but if I am, I would like to know how to go about getting closer to the answer at hand.

Thank you.
 
Physics news on Phys.org
  • #2
EDIT: oops sorry... for some reason I thought the second ball was being thrown down from above. Thanks Astronuc.
 
Last edited:
  • #3
Your solution is correct for finding time, t, which according to your approach is the time after release of the stone. The ball is leading by 0.92 s.

So one has set the height equal and then one solves for the time.

Then pick one of the height equations and solve for the height as a function of the t.

Since one has a quadratic, make sure to pick the correct root.
 
Last edited:

1. What is the "ball freefall problem"?

The ball freefall problem is a physics problem that involves calculating the motion of a ball that is dropped from a certain height under the influence of gravity. It is a commonly used example in physics to illustrate the principles of motion and acceleration.

2. What factors affect the ball's freefall?

The main factor that affects the ball's freefall is gravity. The acceleration due to gravity is constant and is approximately 9.8 m/s^2 on Earth. Other factors that can affect the ball's freefall include air resistance, wind, and the shape and size of the ball.

3. How do you calculate the speed of the ball during freefall?

To calculate the speed of the ball during freefall, you can use the equation v = gt, where v is the final velocity, g is the acceleration due to gravity, and t is the time elapsed. Alternatively, you can use the equation v = √(2gh), where h is the height from which the ball is dropped.

4. What is the relationship between the height and time of a ball in freefall?

The relationship between the height and time of a ball in freefall can be described by the equation h = ½gt^2, where h is the height, g is the acceleration due to gravity, and t is the time elapsed. This equation shows that the height of the ball increases as the square of the time elapsed.

5. How does air resistance affect the ball's freefall?

Air resistance can significantly affect the ball's freefall by slowing down its descent. This is because air resistance is a force that acts in the opposite direction of the ball's motion, and it increases as the speed of the ball increases. Therefore, the ball's speed will decrease as it falls, and it will eventually reach a terminal velocity where the air resistance is equal to the force of gravity.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
229
  • Introductory Physics Homework Help
Replies
4
Views
905
  • Introductory Physics Homework Help
2
Replies
38
Views
1K
  • Introductory Physics Homework Help
Replies
19
Views
951
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
869
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
96
  • Introductory Physics Homework Help
Replies
3
Views
9K
Back
Top