A ball is dropped from the top of a 54.0 m -high cliff. At the same time, a care

Question

A ball is dropped from the top of a 54.0 m -high cliff. At the same time, a carefully aimed stone is thrown straight up from the bottom of the cliff with a speed of 22.0 m/s . The stone and ball collide part way up.

Part A

How far above the base of the cliff does this happen?

A ball is dropped from the top of a 54.0 m -high cliff. At the same time, a carefully aimed stone is thrown straight up from the bottom of the cliff with a speed of 22.0 m/s . The stone and ball collide part way up.

Part A

How far above the base of the cliff does this happen?

Explanation / Answer

let after time t they collide,

so A travels DA = 0.5 x 9.81 x t2

and DB = 22t - 0.5 x 9.81 x t2

=> 0.5 x 9.81 x t2 + 22t - 0.5 x 9.81 x t2 = 54

=> t = 54/22 = 2.454545 sec.

height from base = 22 x 54/22 - 0.5 x 9.81 x (54/22)2 = 24.448 m

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