Ball Freefall Problem: Calculating Distance Traveled by Ball and Stone in m"

In summary: There is no need to check the answer.In summary, a ball is thrown vertically upward with an initial speed of 15 m/s and 0.92 s later, a stone is thrown straight up from the same initial height with an initial speed of 27 m/s. The acceleration of gravity is 9.8 m/s^2. Using the given equations, the time at which the two objects pass each other is approximately 0.4593 seconds. There is no need to check the answer as the displacement of both objects is the same.
  • #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.
 
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  • #2
Sounds right, now just substitute t into one of the equations and get the height - better still do both equations just to check the answer
 
  • #3
AraProdieur said:
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.

Its correct.As the displacement of both the oblects are same you can use the equality among the equations as you have done above.
 

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 or thrown from a certain height. It is also known as the Kinematics problem as it deals with the motion of objects without considering the cause of the motion.

2. What are the key factors that affect the Ball Freefall problem?

The key factors that affect the Ball Freefall problem are the initial height of the ball, the acceleration due to gravity, and the air resistance. Other factors such as the mass and shape of the ball may also have an impact on the problem.

3. How do you calculate the time it takes for a ball to reach the ground in the Ball Freefall problem?

The time it takes for a ball to reach the ground in the Ball Freefall problem can be calculated using the formula t = √(2h/g), where t is the time, h is the initial height, and g is the acceleration due to gravity.

4. Can the Ball Freefall problem be solved using different units of measurement?

Yes, the Ball Freefall problem can be solved using different units of measurement as long as the units are consistent. For example, if the initial height is given in meters, the acceleration due to gravity should also be given in meters per second squared.

5. What are the limitations of the Ball Freefall problem?

The Ball Freefall problem assumes that there is no air resistance and that the acceleration due to gravity is constant. In reality, air resistance can have a significant impact on the motion of the ball, and the acceleration due to gravity may vary slightly depending on the location on Earth. Therefore, the calculations in the Ball Freefall problem may not be entirely accurate in real-life scenarios.

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