Physics Boat Crossing River With Current Question?

Question

Hey everyone, I've got a physics question that sounds easy but keeps showing up as wrong.

In a 500 m stretch of a river, the speed of the current is a steady 5.0 m/s. How long does it take for a boat to finish a round-trip (upstream and downstream) if the speed of the boat is 7.5 m/s relative to still water?

Thanks in advance.

Answer 1

With the upstream:

Velocity of stream + velocity of boat

-5.0 m/s+7.5 m/s=2.5 m/s

Given: Δx=500 m, v0=2.5 m/s, a=0 m/s

xf=x0+vot+(1/2)(a)(t^2)

500m=0m+(2.5m/s)t+(1/2)(0)(t^2)

500 m=(2.5 m/s)(t)

(500 m)/(2.5 m/s) = t

200s=t

Down stream:

Velocity of the river+velocity of boat

5.0 m/s+7.5 m/s=12.5 m/s

xf=x0+vot+(1/2)(a)(t^2)

500m=0m+(12.5 m/s)t+(1/2)(0)(t^2)

500 m=(12.5 m/s)(t)

(500 m)/(12.5 m/s) = t

40 s=t

Time upstream+Time Downstream=Total time

200 s+40 s=240 s