Question

A man sitting in a lift moving upwards with a uniform acceleration f, throws a ball vertically upwards with v as velocity relative to the lift and catches it back after t seconds. Prove that f+g=2v.*​

Answer 1

Appropriate Question:

A man sitting in a lift moving upwards with a uniform acceleration f, throws a ball vertically upwards with v as velocity relative to the lift and catches it back after t seconds. Prove that f+g=2v/t.

Answer:

Let the velocity of the lift be u when ball was thrown.

And the velocity of the ball relative to the lift =v

As we know that,

Relative velocity =( actual velocity of ball - actual velocity of lift)

And,

Actual velocity of the ball is (v+u).

And it is given that the man in the lift catches the ball after t seconds.

Then it is clear that the distance covered by the lift in t seconds with the initial velocity u and acceleration f is equal to the distance covered by the ball in t seconds with initial velocity (v+u) and acceleration (-g).

Therefore by the equation of motion,

ut +1/2at²=(v+u)t-1/2gt²

1/2(f+g)t²=vt

f+g = 2v/t

Hence proved.

Answer 2

Answer:

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