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

Answer:

9.4 m/s

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

$K_f = \frac{1}{2}mv^2$

where:

m = 661 kg is the mass of the car

v is its final speed

Solving, we find

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