# 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?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Trig Review concept. You can view video lessons to learn Trig Review. Or if you need more Trig Review practice, you can also practice Trig Review practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Moussa's class at UCF.