A projectile is projected with a linear momentum p making an angle theta with the horizontal The magnitude of - Physics - Motion In A Plane

Question

​A projectile is projected with a linear momentum p making an
angle theta with the horizontal The magnitude of change in momentum
of the projectile when it returns to the ground will be ?

Vipra Mishra · Accepted Answer

Dear Student

Let’s assume that initial velocity of the
particle is
ui = u cosθ
i + u sin θ j
Here, positive j axis is taken as vertically
upward

In projectile motion, vertical component of
velocity changes but horizontal component of velocity remains
always constant
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_5777ec447abd9%20png"
style="width: 275px; height: 189px;">
Therefore, final velocity of the particle when
it landed on the ground after completing it motion can be written
as
uf
= cosθ i - u sin θ
i

Therefore magnitude of the change in velocity
when particle lands on the ground
Δ u
= uf -ui

Δ u
= -2 u sin θ

Hence change in momentum can be be given
as
Δ p
= -2 mu sin θ

Regards

​A projectile is projected with a linear momentum p making an angle theta with the horizontal. The magnitude of change in momentum of the projectile when it returns to the ground will be ?

A projectile is projected with a linear momentum p making an angle theta with the horizontal. The magnitude of change in momentum of the projectile when it returns to the ground will be ?