A boat leaves a dock and follows a two-leg journey across a lake
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A boat leaves a dock and follows a two-leg journey across a lake.
Leg 1: It travels 5.0 km at a heading of 30∘ north of east at a constant speed of 12 km·h−1.
Leg 2: It immediately changes course and travels 4.0 km at a heading of 60∘ west of north at a constant speed of 8.0 km·h−1.
Respond to each part in a clear, organized manner. Include vector component diagrams or calculations as needed.
(1) Resolve each leg of the trip into east–west (x) and north–south (y) displacement components.
(2) Determine the magnitude and compass bearing of the boat’s net displacement relative to the dock.
(3) Calculate the total time required for the trip.
(4) Compute the magnitude and compass bearing of the boat’s average velocity for the entire trip.