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

AI Thread Summary
The discussion revolves around finding the intermediate height of a ball (hB) in relation to its maximum height (hA) using kinematic equations. The initial assumption that the initial velocity (v0) is zero was identified as incorrect, leading to an erroneous result of hB = 1/9 hA. By applying the SUVAT equations starting from the peak of the ball's trajectory, the correct relationship was derived as hB = 5/9 hA. Participants emphasized the importance of correctly identifying initial conditions and suggested including a diagram for clarity in future problems. This approach significantly improved the understanding and solution of the problem.
SelzerRS
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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
IMG_4786.jpeg

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?
IMG_4788.jpeg
 
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SelzerRS said:
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.

SelzerRS said:
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.
SelzerRS said:
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?
 
jbriggs444 said:
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!!
 
jbriggs444 said:
It took a couple tries for me to read through this successfully.
👆

In the future perhaps just immediately add a correct diagram.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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