# What time are two thrown balls at the same height?

• Yae Miteo
In summary: 10 seconds has passed since the first ball was thrown, so the blue ball is thrown 0.6 seconds after the red ball.
Yae Miteo

## Homework Statement

A red ball is thrown down with an initial speed of 1.2 m/s from a height of 25 meters above the ground. Then, 0.6 seconds after the red ball is thrown, a blue ball is thrown upward with an initial speed of 23.8 m/s, from a height of 0.8 meters above the ground. The force of gravity due to the Earth results in the balls each having a constant downward acceleration of 9.81 m/s2.

How long after the red ball is thrown are the two balls in the air at the same height?

## Homework Equations

$$x = x_o + v_ot + (1/2)at^2$$

## The Attempt at a Solution

I tried setting two different versions of this equation equal to each other; one with information for the blue ball and one with information for the red ball, and then solve for time. I believe that I'm on the right track but that I'm somehow not properly figuring out the time offset for the blue ball. Any suggestions?

Yae Miteo said:
I tried setting two different versions of this equation equal to each other; one with information for the blue ball and one with information for the red ball, and then solve for time. I believe that I'm on the right track but that I'm somehow not properly figuring out the time offset for the blue ball. Any suggestions?
Yes, you're on the right track. Let t be the time as measured from when the red ball was thrown. In terms of t, what is the time from when the blue ball is thrown?

Would it be $$t + 0.6$$ ?

Yae Miteo said:
Would it be $$t + 0.6$$ ?

If t is the time after the red ball is thrown and T is the time after the blue ball is thrown, then can you find the relationship between t and T?

Yae Miteo said:
Would it be $$t + 0.6$$ ?
No. Note that the second ball is not thrown until 0.6 seconds after the first. So, for example, if 10 seconds has passed since the first ball was thrown (thus t = 10), how long ago was the second ball thrown?

## What is the concept of "thrown balls at the same height"?

The concept of "thrown balls at the same height" refers to two objects being launched or thrown from the same location with the same initial velocity and reaching the same height at some point during their trajectory.

## Why is it important to study the time at which two thrown balls reach the same height?

Studying the time at which two thrown balls reach the same height can help us understand the laws of motion and gravity. It also has practical applications in fields such as sports, engineering, and physics.

## What factors affect the time at which two thrown balls reach the same height?

The time at which two thrown balls reach the same height is affected by factors such as initial velocity, angle of launch, air resistance, and the acceleration due to gravity. These factors can vary for different objects and can impact the time it takes for the balls to reach the same height.

## Can two balls thrown at the same height ever reach the same height at the same time?

Yes, it is possible for two balls thrown at the same height to reach the same height at the same time. This can happen if the balls have the same initial velocity and launch angle, and there is no air resistance present.

## How can the time at which two thrown balls reach the same height be calculated?

The time at which two thrown balls reach the same height can be calculated using the equations of motion and considering the factors mentioned above. The time can also be measured experimentally by launching the balls and recording the time it takes for them to reach the same height.

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