Question

Sheena can row a boat at 2.20 mi/h in still water. She needs to cross a river that is 1.20 mi wide with a current flowing at 1.60 mi/h. Not having her calculator ready, she guesses that to go straight across, she should head upstream at an angle of 25.0° from the direction straight across the river.

Answer 1

Answer:

Part a)

$v_{bw} = 2.1 mph$

Part b)

$t = 0.6 h$

Part c)

$x = 0.4 mile$

Part d)

$\theta = 46.6 degree$

Explanation:

Part a)

Velocity of the boat with respect to water stream is given as

$v_{bw} = v_b + v_w$

$v_{bw} = (1.60 - 2.20sin25) \hat i + 2.20 cos25\hat j$

so we have

$v_{bw} = 0.67 \hat i + 2 \hat j$

magnitude of the speed is given as

$v_{bw} = \sqrt{0.67^2 + 2^2}$

$v_{bw} = 2.1 mph$

Part b)

Time to cross the river is given as

$t = \frac{y}{v_y}$

$t = \frac{1.20}{2}$

$t = 0.6 h$

Part c)

Distance moved by the boat in downstream is given as

$x = v_x t$

$x = 0.67 \times 0.6$

$x = 0.4 mile$

Part d)

In order to go straight we must net speed along the stream must be zero

so we will have

$vsin\theta = v_w$

$2.20 sin\theta = 1.60$

$\theta = 46.6 degree$