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Problem: A novice golfer on the green takes three strokes to sink the ball. The successive displacements of the ball are 4.00 m to the north, 2.00 m northeast (45°), and 1.00 m at 30.0° west of south. Starting at the same initial point, an expert golfer could make the hole in what single displacement?

FREE Expert Solution

The magnitude of a resultant vector is:

|R|=|A|2+|B|2+2|A||B|cosθ, where θ is the angle between the two vectors A and B.

We're told that the golfer is taking three strokes, A, B, and C to sink the ball. 

These points in their components can be taken to be:

(Ax, Ay), (Bx, By), and (Cx, Cy).

Vector C is making an angle of 30.0° west of south.

The resultant of these three vectors will have components (Ax + Bx + Cx, A+By + Cy)

The components of A:

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Problem Details

A novice golfer on the green takes three strokes to sink the ball. The successive displacements of the ball are 4.00 m to the north, 2.00 m northeast (45°), and 1.00 m at 30.0° west of south. Starting at the same initial point, an expert golfer could make the hole in what single displacement?

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