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

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`

Step-by-step 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) = √(0.67^2 + 2^2)`

`v_(bw) = 2.1 mph`

Part b)

Time to cross the river is given as

`t = (y)/(v_y)`

`t = (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 * 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`