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A novice golfer on the green takes three strokes to sink the ball. The successive displacements are 4.10 m to the north, 1.90 m northeast, and 1.00 m at 25.0° west of south. Starting at the same initial point, an expert golfer could make the hole in what single displacement?

___ m

____ north of east

I'm stuck on this problem and don't know how I would go about solving this problem. Could someone explain how to solve it with steps for me, I'm mostly interested in understanding how to do this rather than just getting the answer.

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Hi Julian, and welcome to Physics Stack Exchange! I'm glad that you were able to figure out how to solve your problem, but for future reference, this is a site for conceptual questions about physics, not general homework help. Posting a homework problem and asking for someone to demonstrate a solution is not appropriate; you should narrow it down to the specific concept confusing you and ask about that. See our FAQ and homework policy for more information. –  David Z Sep 10 '12 at 1:29
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closed as too localized by David Z Sep 10 '12 at 1:27

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1 Answer

up vote 1 down vote accepted

(1) express each displacement as a two-component xy vector where x is east and y is north*.

(2) find the resultant vector by adding the three vectors together. This is done by adding all of the x components together and then all of the y components together.

(3) convert the resultant vector to polar coordinates to find the distance and angle.

*For example, the 3rd displacement vector is 1.00 m long and has an angle of -115 degrees (south is -90 degrees). The x and y components are:

$x_3 = 1.00m \cdot \cos(-115^\circ) = -0.4226m$

$y_3 = 1.00m \cdot \sin(-115^\circ) = -0.9063m$

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Thank you so much! This helped me figure out how to do this and now understand the process on how to do it. –  Valrok Sep 9 '12 at 23:39
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