Trig Review Video Lessons

Concept

# 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:

$\overline{){\mathbf{|}}{\mathbf{R}}{\mathbf{|}}{\mathbf{=}}\sqrt{\mathbf{|}\mathbf{A}{\mathbf{|}}^{\mathbf{2}}\mathbf{+}\mathbf{|}\mathbf{B}{\mathbf{|}}^{\mathbf{2}}\mathbf{+}\mathbf{2}\mathbf{|}\mathbf{A}\mathbf{|}\mathbf{|}\mathbf{B}\mathbf{|}\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{\theta }}}$, 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:

99% (35 ratings)
###### 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?