Question

A roller coaster moves 85m horizontally, then travels 45m at an angle of 30 degrees above the horizontal. What is its displacement from its starting point?

Answer 1

`vecx=126/_10,28^@ m`

Explanation:

Drawing the sketch and filling in all the data, we observe that it is a closed triangle where the cosine rule is valid to find the required side for the magnitude of the displacement.
This yields :

`x^2=85^2+45^2-2(85)(45)cos150^@`

Solving we get `x=126m`

Then to find the direction of the displacement, we may use the sine rule or the cosine rule in the same triangle to yield that the angle of displacement from the horizontal is `10,28^@`.