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Answer to Question #2803 in Mechanics | Relativity for zizi

Question #2803
A ball is thrown vertically upward with un initial speed of 20 m/s .Two second later a stone is thrwon vertically from the same initial height as the ball with an initial speed of 24 m/s .At what height above the release point will the ball and stone pass each other ?
Expert's answer
Assume that the release level is at y = 0.
Then the y-coordinate of a ball is changed by the following formula:
y = 20 t – ( 9.8 * t2 ) /2
while for the stone its y-coordinate changes as follows:
y = 24(t-1) -( 9.8 * (t-1)2 ) /2 = 24t – 24 – (9.8*t2)/2 + 9.8 t – 9.8/2 = -28.9 + 33.8 t – (9.8*t^2)/2

First we will find t for which the ball and stone pass each other:
20 t – ( 9.8 * t^2 ) /2 = -28.9 + 33.8 t – (9.8*t^2)/2

20 t = -28.9 +33.8 t
13.8 t = 28.9
t = 28.9 / 13.8 ≈ 2.094

Hence the height above the release point will the ball and stone pass each other is equal to
20 *2.094 – ( 9.8 * 2.094^2 ) /2 = 41.88 – 21.4857 = 20.3943

Answer: h= 20.3943.

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