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

(a) 14.5 m/s

(b) 9.5 m/s

Explanation:

Let the speed of the boat in the still water (i.e relative to ground) is .

Given that the speed of the boat relative to water, m/s.

Speed of the water current of the river relative to the ground, m/s towards east.

(a) When the boat is heading toward the east (in the same direction of the current of the river)

The relative velocity, , of the boat with respect to ground is

m/s

Hence, the boat's speed relative to the ground when it is heading east, with the current, is 14.5 m/s.

(b) When the boat is heading toward the west (in the opposite direction of the current of the river)

The relative velocity, , of the boat with respect to ground is

m/s

Hence, the boat's speed relative to the ground when it is heading west, against the current, is 9.5 m/s.

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