What is the height of a ball after being in the air for T/4 seconds?

[robax25]

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.

Homework Equations

y=vot +0.5 at²

The Attempt at a Solution

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

 

[stockzahn]

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.

Homework Equations

y=vot +0.5 at²

The Attempt at a Solution

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

What answer do you get? Please show.

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

 

[robax25]

t/2 second

 

[stockzahn]

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?

 

[robax25]

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]

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]

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]

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.