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Old Oct 12th 2017, 05:29 AM   #1
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Help with Mechanics Question

A ball is thrown vertically up from the ground with a speed v0. At the same instant, a second ball is dropped from rest from a height H, directly above the point where the ball was thrown.
There is no air resistance.
i) Find the time at which the two balls collide.
ii) Find the value of H, in terms of v0 and g, such that at the instant when the two balls collide, the first ball is at the highest point of its motion.

I'm struggling with part i). I've tried considering different Frames of Reference to make it easier but I still know how to work it out.
Any help would be greatly appreciated!
Thanks
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Old Oct 12th 2017, 06:10 AM   #2
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So what have you tried?

You can write equations of motion for each ball.

This will give you several equations.

Some of the terms in these equations will be common.

Choosing the right ones will lead to a pair of simultaneuos equations in two unknowns.

What values do you know about the motion of each ball?
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Old Oct 12th 2017, 06:43 AM   #3
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thrown ball position as a function of time

$y_1 = v_0 t -\dfrac{1}{2}gt^2$

dropped ball position as a function of time

$y_2 = H - \dfrac{1}{2}gt^2$


When they collide, the two balls are at the same position at the same time ...
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