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:

According to the work-energy theorem, the work done on the car is equal to its variation in kinetic energy, so:

$W=K_f - K_i$

where in this problem:

W = -36,733 J is the work done on the car (negative because the car is slowing down)

$K_f$ is the final kinetic energy of the car

$K_i=66,120 J$ is its initial kinetic energy

Solving for Kf,

$K_f = K_i + W = 66,120 +(-36,733)=29,387 J$

Now we can find the final speed of the car by writing the formula for the kinetic energy:

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

where:

m = 661 kg is the mass of the car

v is the final speed

K = 29,387 J is the kinetic energy

Solving for v,

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