Question

You are riding a 450-kg horse at 14.4 km>h east along a desert road. You have inertia equal to 60.0 kg. A police officer driving past (whom you know and who knows your inertia and the horse’s inertia) measures your speed relative to the police car and calculates your kinetic energy to be 16.32 kJ. What possible speed(s) could the police car have been driving at the instant the officer measured your speed?

Answer 1

`v_(p1)` = 19.32 m/s and
`v_(p2)` = 27.32 m/s

Step-by-step explanation:

The kinetic energy has as formula

K = ½ m v²

Where m is the mass and v the speed of the body.

If the policeman calculates the kinetic energy, let's clear the speed

v = √ 2K/m

Let's reduce the units to the SI system

K = 16.32 KJ (1000 J / kJ) = 16.32 10³ J

Let's calculate

v = RA (2 16.32 10 3/60)

v = 23.32 m / s

The rider at 14.4 km/h, reduce

`v_(h)` = 14.4 km / h (1000m / 1km) (1h / 3600s) = 4.00 m / s

We already have the relative speed of the two (rider and police car) which is 23.32, we also have the rider speed 4.0 m / s, let's calculate the possible police speeds

These two speeds come from going in the same direction or in opposite directions

`v_(r)` =
`v_(h)` ±
`v_(p)`

`v_(p)` =
`v_(r)` - vj

`v_(p1)` = 23.32 - 4

`v_(p1)` = 19.32 m/s

`v_(p2)` =
`v_(r)` + vj

`v_(p2)` = 23.32 +4

`v_(p2)` = 27.32 m/s