Question

Please help!!! A river has a constant current of 3 km per hour. If a motorboat, capable of maintaining a constant speed of 20km per hour, tries to reach a point directly opposite the dock, what will his actual speed and direction be? If the river is 2 km wide, how long will it take to cross?

Answer 1

Using the drawing provided by perl, you can see how your vectors form a right triangle. The first thing you should know about a right triangle is the Pythagorean theorem, \[a^2+b^2=c^2 \rightarrow c=\sqrt{a^2+b^2}\].
By calculating the length of the hypotenuse and figuring out the time it takes to traverse that distance at 20kmh, you will know how long it took. You may also recall that the angle theta can be determined by SOH/CAH/TOA to say that the sin(theta)=opp/hyp, so the arcsin(opp/hyp)=theta.
Now you know your direction, speed, distance, and time. :)