Swimming the river
Bill and Phil are standing on one side of the river, chatting, when Jill appears directly opposite them on the other side. The river is 100 feet wide and the section is straight as an arrow.
"Whoever swims to me fastest takes me to dinner tonight!" she says.
Bill and Phil both swim at exactly 5 feet per second (in still water). The current is flowing downstream at 3 feet per second.
They both dive in simultaneously. Bill swims at an angle so that the current's flow is neutralized and he travels horizontally, thus his horizontal component of motion is less than 5 ft/sec. Phil swims straight across -- thus using the entire 5 feet per second of horizontal motion -- and after he reaches the far bank he then swims directly upstream to make up for the distance the current carried him downstream.
Who reaches Jill first?
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1 solution
Using the Triangle of Forces, we can see that Bill's horizontal speed is 4 ft/sec. He therefore travels straight across and reaches Jill in 100/4 = 25 sec.
Phil reaches the far bank in 100/5 = 20 sec. But he is carried downstream (20 * 3) = 60 ft. Swimming directly against the current, he travels at 2 ft/sec, so it takes him an additional (60/2) = 30 sec to reach Jill. Total time = 50 sec.