A hovercraft of mass 83.0 kg can move on a horizontal surface, the x-y plane. A single unbalanced force acts on the hovercraft, but the size of the force is unknown. The hovercraft initially has a velocity of 4.0 m/s in the positive x direction and some time later has a velocity of 7.0 m/s in the positive y direction. How much work is done on the hovercraft by the force during this time?

1369.5 J

Explanation:

According to the work-energy theorem, the work done on an object is equal to the change in kinetic energy of the object itself.

Therefore, we can write:

where:

W is the work done on the hovercraft

m = 83.0 kg is the mass of the hovercraft

u = 4.0 m/s is the initial velocity (in the positive x-direction)

v = 7.0 m/s is the final velocity (in the positive y-direction)

Here the direction of motion of the hovercraft has changed; however, we can ignore this fact, since work is a scalar so the direction of the velocity does not matter.

Therefore, the work done by the force is:

the force on the thing and the distance the force moves the thing