A roller coaster travels 38.8 m at an angle of
14.0◦
above the horizontal.
How far does it move horizontally?
Answer in units of m

Question

A roller coaster travels 38.8 m at an angle of
14.0◦
above the horizontal.
How far does it move horizontally?
Answer in units of m

anonymous · Answer

This is a vectors problem. We are given magnitude (38.8) and direction (14.0°). We solve this by solving for the x-component of the vector.

If x = x-component, y = y-component, M = magnitude, and D = Direction,

$$x = M \cos D $$
$$y = M \sin D$$

So we plug in to the x one:

$$x = M \cos D$$
$$x = 38.8 \cos (14.0°)$$
$$x  \approx37.65$$

The roller coaster traveled about 37.65 meters horizontally.

anonymous · Answer

thx