Question

A particle of mass m is projected from origin O with speed u at an angle theta with positive x-axis. Positive y-axis is in vertically upward. Direction. Find the angular momentum of particle at any time t about O before the particle strkes the ground again.

Answer 1

A particle of mass m is projected from origin O with speed u at an angle theta with positive x-axis. Positive y-axis is in vertically upward direction. the angular momentum of particle at any time t about O before the particle strikes the ground again is =

final speed before hitting the ground will again be u.

resolving into components we have velocities- ucosΘ  along x-direction and usinΘ  along vertically downward direction

we know, angular momentum, L = m[r X v],

here

L=m[rX ucosΘ] +m[r x usinΘ]

or L=mrucosΘsin0 +mrusinΘsin90

i.e L=0+mrusinΘ

therefore required angular momentum is mrusinΘ