A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height . Find the ratio of the times in which it is at height while going up and coming down respectively.

Question

A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height . Find the ratio of the times in which it is at height  while going up and coming down respectively.

Canvas Classes · Accepted Answer

🧠 Ball at the Same Height Twice — Solve the Quadratic for Both Times

Read it. A ball is thrown up with some velocity . It reaches maximum height , so . The ball passes through height  twice — once on the way up, once on the way down. Find the ratio of these two times (measured from launch).

The trick:  is a quadratic. Setting  gives a quadratic in  with two roots — the early one (going up) and the later one (coming down).

First move: set up the quadratic and use the quadratic formula. Both r

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