A boat, whose speed in still water is 2.80m/s , must cross a 280m wide river and arrive at a point 120m upstream from where it starts. To do so, the pilot must head the boat at a 45.0 degrees upstream angle. What is the speed of the river's current?

Answer 1

Well, if he is going upstream, his boat velocity relative to water is 2.80cos45.

Watervelocity-boatveloicy=ground speed

so we need ground speed. WE know how far he went 120, but time. Well, easy. Going across the river, he went 280m with a velocity of 2.80sin45. So time in the water is 280/2.8sin45= 141 (check that) seconds

water velocity= ground speed+boatvelocity
water velocity= 120/141 m/s - 2.8*.707
and you can find it from that.
The negative means it is going opposite to the boat direction