Vector Addition. Where did I go wrong?

[Scorry]

Homework Statement

A car is driven 225 km west and then 98 km southwest (45 degrees). What is the displacement of the car from the point (magnitude and direction)? Draw a diagram.

Homework Equations

Vectors have magnitude and direction.

The Attempt at a Solution

My attempt is attached. This a homework problem. My textbook only has the answer as : 302 km, 32° south of west. What am I doing wrong ?

 

[andrewkirk]

In calculating $D_R$ you did $(156^2-69^2)$ instead of $(156^2+(-69)^2)$

 

[Scorry]

Thanks for the response. In my Ti 89 that gives me a magnitude of 170.578 Km. Did you get 302 km?

 

[SammyS]

Thanks for the response. In my Ti 89 that gives me a magnitude of 170.578 Km. Did you get 302 km?

The 156 is also incorrect.

45° is not consistent with 180°.

By the way: Welcome to PF !

 

[Chestermiller]

The sign of D1x is wrong. From the diagram, you can see that if is -225.

Chet

 

[andrewkirk]

You can make it a lot easier on yourself by leaving the trig until the very last step when you work out the direction of the resulting vector. All the rest can be done by Pythagoras Theorem. Work out the vert and horizontal components of the 98km vector as each $\frac{98km}{\sqrt{2}}$, then add each to the vert and horiz components of the 225km vector. Then use Pythag to calc the length of that resulting vector from its V and H components. The direction is then calculated as $\arctan\frac{vertical\ compt}{horiz\ component}$. You may need to add or subtract that from 180 degrees, but it will be obvious from the diagram what you need to do, once you've got the angle.