Precalc
posted by Natalie .
A boat that travels at 16 knots in calm water is sailing across a current of 3 knots on a river 250 m wide. The boat makes an angle of 35 degrees with the current heading into the current.
Find the resultant velocity of the boat. How far upstream is the boat when it reaches the other shore?
Do I need to use parametric equations to solve this? If so, how do I find the time? Thanks in advance.

Boat velocity component upstream = 16 cos 35  3
= 13.1  3
= 10.1 kn
Boat velocity component across stream = 16 sin 35 = 9.18 kn
resultant speed = sqrt(10.1^2+9.18^2) = 13.6 kn
tangent of resultant angle to upstream = 9.18/10.1 = .909
so angle to upstream = tan^1 .909 = 42.3 deg
Now you do not have to know time T because
distance upstream = 10.1 T
distance across = 9.18 T
distance upstream/distance across =10.1/9.18 (The T cancels
so
10.1/9.18 = distance upstream/250 meters
so
distance upstream = 250 * 10.1/9.18 = 275 meters
That avoids having to convert nautical miles to meters. I suppose in a sense my use of T implies parametric :)