General physics problem?

Question

A roller coaster car moves 200ft horizontally and then rises 135ft at an angle of 30deg above the horizontal. It then travels 135ft at 40deg downward.

What is the displacement from its starting point?

[diagram]: http://i82.photobucket.com/albums/j264/umyeahyourmom/Untitled.jpg

Answer 1

The horizontal displacement is:

200 + 135(cos(30) + cos(40)) = 420.33 m.

The vertical displacement is:

135(sin(40) - sin(30)) = 19.28 m. (down).

The displacement magnitude is:

sqrt(420.33^2 + 19.28^2)

= 421m.

The angle below the horizontal is x where:

tan(x) = 19.28 / 420.33

x = 2.63 deg.