1. ## problem

A boat that travels at the speed of 6.75 m/s in still water is to go directly across a river and back. The current flows at 0.50 m/s. (a) At what angle(s) must the boat be steered? (b) How long does it take to make the round trip? (The width of the river is 150 meters. Assume that the boat's speed is constant at all times, and neglect turnaround time.)

2. Originally Posted by Celia
A boat that travels at the speed of 6.75 m/s in still water is to go directly across a river and back. The current flows at 0.50 m/s. (a) At what angle(s) must the boat be steered? (b) How long does it take to make the round trip? (The width of the river is 150 meters. Assume that the boat's speed is constant at all times, and neglect turnaround time.)
Hello,

the direction perpendicular to the shore(s) has a bearing of 0°.

The way of the boat through the water, the current of the river and this perpendicular direction form a right triangle. (See attachment)

the way per second of the boat over ground is (use Pythagorian Theorem):

$\displaystyle w=\sqrt{(6.75m)^2-(0.5m)^2}\approx 6.73 m$

to a) You have to steer the boat against the current with an angle of:

$\displaystyle \arcsin\left(\frac{0.5}{6.75}\right)\approx 4.25^{\circ}$

on your way back you must steer: 180°-4.25°= 175.75°

to b) The boat has to travel 2 * 150 m = 300 m over ground. The boat travel 6.73 m/s over ground. So it'll take

$\displaystyle t = \frac{300}{6.73}\approx 44.6 s$

Greetings

EB
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