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

9.43 m/s

Step-by-step explanation:

First of all, we calculate the final kinetic energy of the car.

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

`W=K_f - K_i`

where

W = -36.733 J is the work done on the car (negative because the car is slowing down, so the work is done in the direction opposite to the motion of the car)

`K_f` is the final kinetic energy

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

Solving,

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

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

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

where

m = 661 kg is the mass of the car

v is its final speed

Solving for v, we find

`v=\sqrt{(2K_f)/(m)}=\sqrt{(2(29,387))/(661)}=9.43 m/s`