Question

A stone is projected vertically up with a momentum 20 kg m/s. It's momentum at half of of its maximum height is

Answer 1

let initial velocity is u and mass of stone is m.

at maximum height, H, velocity of stone is zero.

use formula, v² = u² + as

or, 0 = u² - 2gH

or, u² = 2gH ..........(1)

velocity of body at half of maximum height.
v² = u² - 2g(H/2)
v² = 2gH - gH = gH ........(2)

from equations (1) and (2),
v² = u²/2 => v = u/√2


now, it is clear that, initial momentum of stone = mu = 20kgm/s
final linear momentum of stone = mv = mu/√2
= 20/√2 = 10√2 kgm/s