# Magnitude of Single Displacement:

1. Jan 27, 2008

### sonastylol

[SOLVED] Magnitude of Single Displacement:

Please bear with me, I'm going to try and properly format this, so you forum-goers actually want to help me out.

1. The problem statement, all variables and given/known data

A novice golfer on the green takes three strokes to sink the ball. The successive displacements are 7.4 m to the north, 2.8 m northeast, and 9.9 m 79degreeswest of south. Starting at the same initial point, an expert (lucky) golfer could make the hole in a single displacement. What is the magnitude of this single displacement? Answer in units of m.

2. Relevant equations

Magnitude = $$\sqrt{(axi)^2 + (ayj)^2}$$

3. The attempt at a solution

For this equation:

Magnitude of A: $$\sqrt{(0)^2 + (7.4)^2}$$
Magnitude of B: $$\sqrt{(2.8cos45)^2 + (2.8sin45)^2}$$

Heres the tricky part:
Vector C is described as 9.9m 79 degrees west of south. Does this make it 191 degrees?
If yes: Vector C should be: $$\sqrt{(9.9cos191)^2 + (9.9sin191)^2}$$

I then add up the values of Magnitude A, B, C to get the answer... yes?

2. Jan 27, 2008

### Kurdt

Staff Emeritus
No you don't add the magnitudes to get the final magnitude. You need to find out what direction he should have hit the ball to make it in one shot and then find the magnitude. Try drawing a diagram it will help.

3. Jan 27, 2008

### sonastylol

i dont exactly understand what we are trying to do anymore then.. the answer isnt the addition of the 3 vectors magnitudes?

Is the answer the magnitude of one "new vector?" -- Like if we make a Vector D and give it an x and y component, from the addition of the first 3 vectors?

4. Jan 27, 2008

### Kurdt

Staff Emeritus
That is correct.

5. Jan 27, 2008

### sonastylol

hmmm... I think maybe my angles are wrong.

I did Vector D x-components: 0 + (2.8cos(45)) + (9.9cos(191))
Vector D y-components: 7.4 + (2.8sin(45)) + (9.9sin(191))

The answer ended up being 10.769.

Thank you :)