Answered: The engine of a boat drives it across a…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter3: Motion In Two Dimensions

Section: Chapter Questions

Problem 1P: A motorist drives south at 20.0 m/s for 3.00 min, then turns west and travels at 25.0 m/s for 2.00...

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Question

The engine of a boat drives it across a river that is 238 m wide. The velocity of the boat relative to the water is 14.2 m/s. The velocity of the water with respect to the shore is 2.7 m/s @ East. The driver of the boat wants to travel straight across the river (north). At what angle should the boat’s velocity be directed so that the boat goes straight across the river (with respect to the +x-axis)? (Use as many sig figs as possible even though its an angle.)

Expert Solution

Step 1

Width of river $(w) = 238 m$

Velocity of boat relative to water $(v_{b w}) = 14.2 m/s$

Velocity of water $(v_{w}) = 2.7 m/s$

Step 2

The velocity of boat relative to water will be given by;

$\vec{v_{b w}} = \vec{v_{b}} - \vec{v_{w}}$

Therefore, velocity of boat relative to shore will be;

$\vec{v_{b}} = \vec{v_{b w}} + \vec{v_{w}}$

Therefore, magnitude of velocity of boat will be;

$∴ v_{b} = \sqrt{v_{b w}^{2} + v_{w}^{2}}$

$∴ v_{b} = \sqrt{{(14.2)}^{2} + {(2.7)}^{2}}$

$∴ v_{b} = 14.45 m/s$

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