Question

An object of mass 10kg is projected with speed 40m/s from ground at an angle 60 degreewith the horizontal. the rate of change of momentum if an object one second after projection

Answer 1

Explanation:

Momentum= mv

At t=0, velocity is 40 m/s. Momentum is - mv=10*40=400kg-m/s

At t=1, velocity will be:

• In vertical direction,

v=u-gt

vᵧ=40 sin 60° - 10(1)

vᵧ=20√3 - 10 = 24.6

• In x direction

vₓ=40 cos 60°=20 m/s

Net velocity= √(   (20)² +  (20√3 - 1017 )²  ) )

                   = 31.73 m/s

So momentum after 1 s= mv= 10*31.73= 317.73 kg-m/s

Change of momentum= final - initial = 317.73-400= -82.27 kg-m/s

Also:

Momentum ∝ Velocity

Rate of change of momentum ∝ rate of change of velocity.

We know v=u-gt

Differentiating by dt,

dv/dt= -g

Rate of change of velocity in projectile motion is -g m/s²

So rate of change of momentum in the above answer is -g m/s²