Question

A car is strapped to a rocket (combined mass = 661 kg), and its kinetic energy is 66,120 J.

At this time, the rocket runs out of fuel and turns off, and the car deploys a parachute to slow down, and the parachute performs 36,733 J of work on the car.

What is the final speed of the car after this work is performed?

Answer 1

9.4 m/s

Step-by-step explanation:

The work-energy theorem states that the work done on an object is equal to the change in kinetic energy of the object.

So we can write:

`W=K_f - K_i`

where in this problem:

W = -36.733 J is the work performed on the car (negative because its direction is opposite to the motion of the car)

`K_i = 66,120 J` is the initial kinetic energy of the car

`K_f` is the final kinetic energy

Solving for Kf,

`K_f = W+K_i = -36,733+66,120=29,387 J`

The kinetic energy of the car can be also written as

`K_f = (1)/(2)mv^2`

where:

m = 661 kg is the mass of the car

v is its final speed

Solving, we find

`v=\sqrt{(2K)/(m)}=\sqrt{(2(29,387))/(661)}=9.4 m/s`