Question

a boat that travels at a speed of 6.75 m/s in still water is to go directly across a river and back . the current flows at 0.50 m/s (a) at what angle(s) must the boat be steered. (b)How long does it take to make a round trip? (assume that the boats speed is constant at all times and neglect turn around time)

Answer 1

If it is to go directly across,then it must be headed upstream.

Theta=arcsin(.5/6.75)

Then velocity across= 6.75*arccosTheta

If you need more assistance, ask a followup question.

Answer 2

say the boat travels at angle T from straight across. Then the upstream component of the boat velocity relative to water must be .5 m/s to counteract current
so 6.75 sin T = .5 m/s
sin T = .5/6.75 = .0741
so T = sin^-1 (.0741) = 4.25 degrees from straight across toward upstream both ways.
The component of velocity across the river is then
6.75 cos 4.25 deg = 6.73 m/s
You did not say how wide the river is so I will call it D
time = 2 D/6.73