Question

Tina can grow a boat at 2.60 mi/h in still water. She needs to cross a river that is 1.20 mi wide with a current flowing at 1.90 mi/h. Not having her calculator she guesses that to go straight across she should head upstream at an angle of 25.0° from the direction straight across the river. What is her speed with respect to the starting point on the bank?

Answer 1

Let the direction of the opposite shore be the +x direction and the direction of upstream be the +y direction

Let V_BW = velocity of boat relative to the water = 2.6 mi/h

V_WS = velocity of the water relative to the shore = 1.9 mi/h

V_BW = 2.6*cos 25 x + 2.6*sin 25 y

V_BW = 2.3564 x + 1.0988 y

V_WS = -1.9 y

V_BS = V_BW + V_WS

V_BS = 2.3564 x + 1.0988 y - 1.9y

V_BS = 2.3564 - 0.8012

V_BS =

V_BS = 2.4888

Velocity of boat relative to the shore V_BS = 2.5 mi/h