A boat can be rowed at 7.7 km/h in still water. (a) How much time (in min) is re

Question

A boat can be rowed at 7.7 km/h in still water.

(a) How much time (in min) is required to row 1.0 km downstream in a river moving 2.4 km/h relative to the shore? (Assume the river is flowing toward the east.) 5.94 min

(b) How much time (in min) is required for the return trip? 11.32 min

(c) In what direction must the boat be aimed to row north straight across the river? (Enter your angle in degrees counterclockwise from the east axis.)

(d) Suppose the river is 0.7 km wide. What is the speed of the boat with respect to Earth (in km/h)? (Assume the boat is aimed in the direction such that it will be rowed straight across the river.)

(d2) How much time (in min) is required to get to the opposite shore?

(e) Suppose, instead, the boat is aimed straight across the river. How much time (in min) is required to get across?

(e2) How far downstream (in km) is the boat when it reaches the opposite shore?

Explanation / Answer

c] To cancel the velocity of river,

Vb* cos theta + Vr = 0

cos theta = -2.4/77

theta = arccos(2.4/7.7)

= 108.16 degree

d] speed of boat with respect to earth = Vb sin 108.16 degree

= 7.7*sin 108.16 degree

= 7.316 km/h

d2] time = 0.7km/(7.316km/h) = 0.09568 h

= 5.74 min

e1] time = 0.7km/(7.7km/h) = 0.090909 h

= 5.454 min

e2] distance = 2.4 km/h *0.090909 h

= 0.218 km

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