If you just want to get to the other side and do not care how far downstream you land, head straight across. That maximizes your speed component perpendicular to the current.
1.5 km * 1 hour/ 8 km = (1.5/8) hours = 11.25 minutes
(5 km/hour)(1.5 /8)hours = 0.9375 km
A man is rowing at 8 km/h in a river 1.5 km wide in which the current is 5 km/h. (a) In what direction should he head in order to get across the river in the shortest possible time? (b) How much time will he take if he goes in this direction? (c) How far downstream will the boat have gone when it reaches the opposite side?
3 answers
a. Vr = Vb + Vc = 8 = Resultant velocity.
Vb + (-5i) = 8,
Vb = 8 + 5i = 9.43km/h[32o] N. of E. = Velocity and heading of boat.
b. d = V * T = 1.5.
8T = 1.5,
T = 0.1875 h.
c. Since the affect of the current is offset by the 32o heading, the boat goes directly across the river.
Vb + (-5i) = 8,
Vb = 8 + 5i = 9.43km/h[32o] N. of E. = Velocity and heading of boat.
b. d = V * T = 1.5.
8T = 1.5,
T = 0.1875 h.
c. Since the affect of the current is offset by the 32o heading, the boat goes directly across the river.
Henry, it said get across as fast as possible. It did not say to go to a point directly across. Your across component is maximum if you ignore the current and head straight across, drifting downstream of course.