As part of an endurance race, Stephanie needs to swim from X to Y across a wide river

Chapter 13, Problem 4

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QUESTION:

As part of an endurance race, Stephanie needs to swim from X to Y across a wide river. Stephanie swims at \(1.8 \mathrm{~m} \mathrm{~s}^{-1}\) in still water. The river flows with a consistent current of \(0.3 \mathrm{~m} \mathrm{~s}^{-1}\) as shown.

a Find the distance from X to Y.

b In which direction should Stephanie aim so that the current will push her onto a path directly towards Y?

c Find the time Stephanie will take to cross the river.

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Questions & Answers

QUESTION:

As part of an endurance race, Stephanie needs to swim from X to Y across a wide river. Stephanie swims at \(1.8 \mathrm{~m} \mathrm{~s}^{-1}\) in still water. The river flows with a consistent current of \(0.3 \mathrm{~m} \mathrm{~s}^{-1}\) as shown.

a Find the distance from X to Y.

b In which direction should Stephanie aim so that the current will push her onto a path directly towards Y?

c Find the time Stephanie will take to cross the river.

ANSWER:

Step 1 of 3

a.)

Let’s draw a diagram as,

Pythagoras' theorem can be used here to determine d as,

\(d = \sqrt {{{20}^2} + {{80}^2}} \)

\(d = \sqrt {6800} \)

\(d = 82.46\;{\rm{m}}\)

\(d = 82.5\;{\rm{m}}\)

Hence, the distance from X to Y is about 82.5 m.

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