Question

A roller-coaster car moves 200 ft horizontally and then rises 135 ft at an angle of 30.0 degrees above the horizontal. It next travels 135 ft at an angle of 40.0degrees downward. What is its displacement from its starting point? Use graphical techniques.

I am stuck on where the roller coaster goes graphically.

Answer 1

To do it graphically, you would plot it like so on graph paper and measure the dotted line.

A nongraphical check of what you should get:

1: +200 x, 0 y

2: +135 y (given component), 30 degree angle => x=135/tan(30)= + 233.827 x

3: 135*cos(-40) = +103.416 x , 135*sin(-40) = -86.776 y

Sum the 3 sets of components: 537.24 x, 48.22 y

Total distance = sqrt(537.24^2 + 48.22^2) = 539.40