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.*
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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.
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