Question

A man wished to travel due north in order to cross river 5kilometer wide flowing due east at 2kilometer per hour. If he can roll at 9kilometer per hour in still water, find 1. The direction in which he must head his boat in order to get to his destination directly opposite to his starting point. 2. The resultant velocity of the boat in the river. 3. The time taken to cross the river.

Answer 1

you have a right triangle, with the hypotenuse = 9 (his actual speed), and one leg=2 (the current)

so, his resultant velocity must be upstream at an angle x such that

sin(x) = 2/9
and the actual resultant speed s (due north) is √(9^2-2^2)

Having gotten his speed s, the time needed is 5/s

Answer 2

1. 2 + 9i = 9.22km/h[77.5o] N. of E. = 12.5o E. of N.
Direction = 12.5o W. of N.

2. Vr = 9.22 km/h(part 1).

3. V*T = d = 5km.
9*T = 5, T = 0.555 h.