Finding the intermediate height of a ball in terms of its maximum height

[SelzerRS]

Homework Statement

A Ball is thrown up from the ground (point O). On its way up it passed a point B. The time it takes to reach B is tB = 1/3 tA. Find the height of OB = hB in terms of OA = hA. (point A is it’s maximum height)

Relevant Equations

y = y0 + v0t - 1/2gt^2
h= 1/2 gt^2
v = v0 + at

Ive done this problem two different ways (sorry it’s messy) and keep getting hB = 1/9 hA, but my homework says it’s wrong. I’m guessing it’s because I assume that v0 is 0, but I’m not sure what other formulas or steps I need to take to either find or omit the variable. Are there any other formulas I need to take into account?

 

[jbriggs444]

Homework Statement: A Ball is thrown up from the ground (point O). On its way up it passed a point B. The time it takes to reach B is tB = 1/3 tA. Find the height of OB = hB in terms of OA = hA. (point A is it’s maximum height)

It took a couple tries for me to read through this successfully. Too many variable names. No matter. I am with you so far.

Relevant Equations: y = y0 + v0t - 1/2gt^2
h= 1/2 gt^2
v = v0 + at

View attachment 350575

It looks like you are trying to do things the obvious way, using the SUVAT equation for the final position, given the initial velocity at time zero (unknown), the acceleration ($g$) and the elapsed time ($t$).

You assume that the initial velocity is zero. But that assumption is obviously incorrect.

And things go downhill from there.

Ive done this problem two different ways (sorry it’s messy) and keep getting hB = 1/9 hA, but my homework says it’s wrong. I’m guessing it’s because I assume that v0 is 0, but I’m not sure what other formulas or steps I need to take to either find or omit the variable. Are there any other formulas I need to take into account?

You are exactly right about the problem with the assumption.

What happens if you apply the same SUVAT equation, but starting from the moment that the ball reaches the peak of its trajectory and working backward?

 

[SelzerRS]

It took a couple tries for me to read through this successfully. Too many variable names. No matter. I am with you so far.


It looks like you are trying to do things the obvious way, using the SUVAT equation for the final position, given the initial velocity at time zero (unknown), the acceleration ($g$) and the elapsed time ($t$).

You assume that the initial velocity is zero. But that assumption is obviously incorrect.

And things go downhill from there.

You are exactly right about the problem with the assumption.

What happens if you apply the same SUVAT equation, but starting from the moment that the ball reaches the peak of its trajectory and working backward?

Thank you so much! I was able to get to hB = 5/9 hA. Setting the peak as the initial velocity really helped!!

 

[erobz]

It took a couple tries for me to read through this successfully.

In the future perhaps just immediately add a correct diagram.