Question

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?

Answer 1

Answer:

(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 $v_0$.

Given that the speed of the boat relative to water, $v_r=12.0$ m/s.

Speed of the water current of the river relative to the ground, $u_0=2.50$ 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, $v_r$, of the boat with respect to ground is

$v_r=v_0-u_0$

$\Rightarrow 12=v_0-2.5$

$\Rightarrow v_0=12+2.5=14.5$ 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, $v_r$, of the boat with respect to ground is

$v_r=v_0-(-u_0)$

$\Rightarrow 12=v_0+2.5$

$\Rightarrow v_0=12-2.5=9.5$ m/s

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