A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground is changed by ________?

Answer:

Let us consider for the first case

Intial velocity (u) = 0

Final velocity (v) = v

Height (h) = h

Acceleration (a) = g

Momentum (p1) = mv

Let us consider for the second case

Intial velocity (u) = o

Final velocity (v) = v’

Height (h) = h’

Acceleration (a) = g

Momentum (p2) = mv’

Now consider

Velocity v = √2gh………………………….(1)

Momentum p = mv…………………………..(2)

From equation (1) and (2) we observe that

p ∝ √h

Here,

p2/p1= √h’/h

p2/p1= √2h/h

p2/p1= √2

p2=1.414p1

% change = (p2 – p1)/p1 × 100

% change = =41%

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