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Two boats start together and race across a 56 km wide lake and back. Boat A goes across at 56...

Question:

Two boats start together and race across a 56 km wide lake and back. Boat A goes across at 56 km/h and returns at 56 km/h. Boat B goes across at 28 km/h, and its crew, realizing how far behind it is getting, returns at 84 km/h. Turnaround times are negligible, and the boat that completes the round-trip first wins.

a) Which boat wins? (or is it a tie?)

b) By how much?....km

c) What is the average velocity of the winning boat? ....km/h

Uniform motion problems:

When the speed of a body during motion remains constant, it is said to be in uniform motion. In uniform motion we use the relation: {eq}s = v*t {/eq}, where s is the distance traveled, v is the speed and t is the time taken.

Answer and Explanation:

1.

Boat A

  • time while reaching across the lake = {eq}\frac{s}{v} = \frac{56}{56} = 1 {/eq}hour
  • time while returning = {eq}\frac{s}{v} = \frac{56}{56} = 1 {/eq}hour

total time = 1 + 1 = 2 hour

Boat B

  • time while reaching across the lake = {eq}\frac{s}{v} = \frac{56}{28} = 2 {/eq}hours

Clearly, Boat A has returned back in 2 hours whereas Boat B has only reached across the lake. So, Boat A is the winner.

2. Boat A wins by the width of the lake, i.e 56 km.

3. Average velocity of the winning boat = {eq}\frac{\text{net displacement}}{\text{total time}} {/eq}.

Boat A starts its motion, returns back and ends it at the same starting point. Hence the initial and the final positions of the boat A are the same. So, net displacement is zero. Thus, from the above formula, the average velocity will be zero.


Learn more about this topic:

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How to Solve Uniform Motion Problems

from Saxon Algebra 1 Homeschool: Online Textbook Help

Chapter 10 / Lesson 5
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