please help me out with this hard physics problem?

Question

a river flows south at 3m/s and is 50 m wide. An intrepid beaver sets out from west shore, aiming himself directly east. He swims with velocity relative to the water of 2m/s, east.
how long to cross stream
velocity
how far downstream
how long to cross river when dam is broke and velocity is 25m/s

Answer 1

This is a vector problem.

The beavers velocity is always 2m/sec in the easterly direction regardless of everything else.

Since the river is 50 m wide, it takes 25 secs to cross
t=d/v

Now, to figure out the velocity, you need your Pythagorean theorem. a^2+b^2=c^2 where a and b are the velocities east and south, respectively.

For how far downstream you need the time to cross the river and the southbound velocity. Dsouth=t*Vsouth

As for the dam breaking, you have the same velocity east so nothing changes.

Plug&chug to get the answers.

Answer 2

use the kinematics equations and laws of sines and cosines