Question

A problem about the work done by gravity on a projectile?

A projectile of mass m = 0.200 kg is fired at an angle of 60.0 degrees above the horizontal
with a speed of 20.0 m/s. Find the work done on the projectile by the gravitational force
during its flight from its firing point to the highest point on its trajectory

Answer 1

Given mass of the projectile `m=0.2kg`

Velocity of projection `u=20.0ms^-1`

Angle of projection with horizontal `alpha=60^@`

Vertical component of velocity of projection `v=usinalpha=20xxsin60^@=10sqrt3ms^-1`.

The gravity will influence the vertical component only and it will be diminished at the the rate of acceleration due to gravity `g=9.8ms^-2` and will be zero at the top of the trajectory.
So the decrease in vertical kinetic energy will determine the work done on the projectile by the gravitational force during its flight from its firing point to the highest point on its trajectory.

Hence this work done

`W=1/2mv^2=1/2xx0.2xx(10sqrt3)^2=150J`