Question

A canoeist can paddle a maximum speed of 6.4 m/s in still water. The canoeist starts on the north shore of the river and attempts to paddle to the south shore 225m away, the river is flowing 2.45m/s [E]. the canoeist always remains at a right angle to the north shore.
Determine the resultant velocity of the canoeist, relative to the shore.

Answer 1

Answer on Question#53249 - Physics - Mechanics - Kinematics - Dynamics

A canoeist can paddle a maximum speed of $v = 6.4 \, \text{m/s}$ in still water. The canoeist starts on the north shore of the river and attempts to paddle to the south shore $225 \, \text{m}$ away, the river is flowing $v_{\parallel} = 2.45 \, \text{m/s}$ [E]. The canoeist always remains at a right angle to the north shore. Determine the resultant velocity of the canoeist, relative to the shore.

Solution:

Since the canoeist remains at a right angle to the north shore, the west component of his velocity (which compensates the flow of the river) is equal to the speed of the river $(2.45\mathrm{m/s})$. Therefore its net velocity is given by

$$v_{\perp} = \sqrt{v^{2} - v_{\parallel}^{2}} = \sqrt{\left(6.4 \, \frac{\mathrm{m}}{\mathrm{s}}\right)^{2} - \left(2.45 \, \frac{\mathrm{m}}{\mathrm{s}}\right)^{2}} = 5.91 \, \frac{\mathrm{m}}{\mathrm{s}}$$

Answer: $5.91 \, \frac{\mathrm{m}}{\mathrm{s}}$.

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