Question

A police officer is driving due north at a constant speed of 29 m/s relative 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 triangle 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 velocity relative to the police car. The sketch need not be to scale, but the velocity vectors should be oriented correctly and bear the appropriate labels.

(b) What is the truck’s speed, relative to the ground?

Answer 1

Step-by-step explanation:

Velocity of police officer with respect to ground V(p,g) = 29 j m/s

Velocity of truck with respect to police officer, V(t,p) = 48 (-i) m/s

(a) Figure is attached

(b)

Velocity of truck with respect to police officer = Velocity of truck with respect to ground - Velocity of police officer with respect to ground

- 48 i = velocity of truck with respect to ground - 29 j

Velocity of truck with respect to ground = - 48 i + 29 j

Velocity of truck with respect to ground =
`\sqrt{48^(2)+29^(2)}` = 56.08 m/s