# Throwing a ball upwards

## Homework Statement

A child tosses a ball directly upward. Its total time in the air is T. Its maximum height is H. What is its height after it has been in the air a time T/4? Neglect air resistance.

y=vot +0.5 at²

## The Attempt at a Solution

It is 1/4 H but I don't get exact answer.

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stockzahn
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Gold Member

## Homework Statement

A child tosses a ball directly upward. Its total time in the air is T. Its maximum height is H. What is its height after it has been in the air a time T/4? Neglect air resistance.

y=vot +0.5 at²

## The Attempt at a Solution

It is 1/4 H but I don't get exact answer.

At what time do you think the ball reaches the maximal height H?

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t/2 second

stockzahn
Homework Helper
Gold Member
t/2 second
What value are you able to obtain with that information and the equation you posted in section 2 of the template in your first post?

y=v(t/2)-0,5a(t/2)² when the ball is at maximum height and vo is equal to gt/2

Ray Vickson
Homework Helper
Dearly Missed
y=v(t/2)-0,5a(t/2)² when the ball is at maximum height and vo is equal to gt/2
So, you can find $t$ from the first equation (using $y = H$, a given input in the problem); then, after finding $t$ you can figure out $v_0$. Take it from there.

By the way: either use $g$ or $a$, but not both notations in the same problem, given that they are both supposed to be the same quantity.

stockzahn
Homework Helper
Gold Member
y=v(t/2)-0,5a(t/2)² when the ball is at maximum height and vo is equal to gt/2
Stay with the definition that $v_0$ is the velocity of the ball when it leaves the child's hand, which is what you want to calculate to find the answer of the original problem ($v_0=f\left(g, T, H\right)$).

mfb
Mentor
There is no need to find the initial velocity.
t/2 second
What is t? Why did you add "seconds"?
I guess you mean T/2 - just half of the total air time. That is correct.

Consider the second half of the motion for a moment: How can you describe how far it fell down from the highest point as a function if time?
It drops down by H over a time of T/2. How much does it drop down in half of that time, in T/4? While that is not the final answer to the problem you can transfer that result to get the right answer.