Question

A police officer is driving due north at a constant speed of 29 m/s rel- ative to the ground when she notices a truck on an east–west highway ahead of her, driving west at high speed. She finds that the truck’s speed relative to her car is 48 m/s (about 110 mph). (a) Sketch the vector trian- gle that shows how the truck’s velocity relative to the ground is related to the police car’s velocity relative to the ground and to the truck’s veloc- ity relative to the police car. The sketch need not be to scale, but the ve- locity vectors should be oriented correctly and bear the appropriate labels. (b) What is the truck’s speed, relative to the ground?

Answer 1

The truck’s speed, relative to the ground = 38.25 ms⁻¹

Step-by-step explanation:

As per the question,

Given data:

Velocity of car with respect to ground = 29 ms⁻¹

Velocity of truck with respect to car = 48 ms⁻¹

so

now

Using the vector sum property in the vector triangle, we can say

`V_(t,g)=V_(t,c)+V_(c,g)`

As we have given the magnitude of velocities

Now,

By using Pythagoras theorem in triangle AOB

OA² + OB² = AB²

OA = √(48² - 29²) = 38.25 ms⁻¹

Therefore, the truck’s speed, relative to the ground = 38.25 ms⁻¹