   Chapter 2, Problem 5P

Chapter
Section
Textbook Problem

Two boats start together and race across a 60-km-wide lake and back. Boat A goes across at 60 km/h and returns at 60 km/h. Boat B goes across at 30 km/h, and its crew, realizing how far behind it is getting, returns at 90 km/h. Turnaround times are negligible, and the boat that completes the round trip first wins. (a) Which boat wins and by how much? (Or is it a tie?) (b) What is the average velocity of the winning boat?

(a)

To determine
The boat which wins and the distance between them.

Explanation

Given Info:

The speed of boat A is 60km/h .

The length of the lake is 60km .

The speed of boat B when moves across the lake is 30km/h .

The speed of boat B when it returns is 90km/h .

Explanation:

The formula used to calculate the time taken by boat A to cross the lake is,

ΔtA=ΔxAvA

• ΔtA is the time taken to go across the lake by boat A
• ΔxA is distance covered by the boat A
• ΔvA is the velocity of boat A

Substitute 60km for ΔxA , 60km/h for vA to find ΔtA .

ΔtA=60km60km/h=1h

The boat A moves across the lake in one hour and returns in next hour

(b)

To determine
The average velocity of the winning boat.

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