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December 20, 2014

December 20, 2014

Posted by **Natalie** on Friday, April 11, 2008 at 12:29pm.

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.

- Precalc -
**Damon**, Friday, April 11, 2008 at 5:55pmBoat 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 :)

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