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Carnegie Mellon University

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Problem 21 Medium Difficulty

Suppose a boat moves at 12.0 $\mathrm{m} / \mathrm{s}$ relative to the water. If the boat is in a river with the current directed east at $2.50 \mathrm{m} / \mathrm{s},$ what is the boat's speed relative to the ground when it is heading (a) east, with the current, and (b) west, against the current?

Answer

(a) $V _ { \mathrm { BG } } = 14.5 \mathrm { ms } ^ { - 1 }$
(b) $V _ { \mathrm { BG } } = 9.5 \mathrm { ms } ^ { - 1 }$ towards the west.

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Video Transcript

so quick, we're gonna say east and north are positive and we're going to say that south and West are negative. So we can then say that the four party the velocity of the boat relative to the ground will be equaling the velocity of the boat relative to the water plus the velocity of the water relative to the ground or this being essentially the current and so for part A this is gonna be equaling positive 12.0 meters per second because the velocity of the boat relatives of the water is positive 12.0 meters per second. When the boat is moving east relative to the water and then plus 2.50 meters per second, that would be the current, and in this case it's working with us. So this would be 14.5 meters per second. This would be our final answer for the velocity of the boat relative to the ground. Now, for part B, we're going to use the exact same relationship, the velocity of the boat relative to the ground, equaling the velocity of the boat relatives of the water plus the velocity of the water relative to the ground over here. Now the velocity of the boat relative to the water is directed west and so this is equaling negative 12.0 meters per second plus 2.50 meters per second. Given that the current is always flowing east and this is giving us negative 9.50 meters per second, this would be our answer for part B. Um 9.50 meters per second is essentially the magnitude. We only say negative because in this case, the velocity of the boat relative to the ground is west. Where here the velocity of the boat relative to the ground is actually east. That is the end of the solution. Thank you for watching.

Carnegie Mellon University
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