A roller coaster travels 350 feet horizontally and then travels 130 feet at an angle of 60⁰ from the ground. What is the magnitude of the resultant vector?

Question

What is the magnitude of the resultant vector?

Answer 1

First we have to understand that there are 2 vectors in this problem.

We can assume that the first vector can be represented as: V₁= 350i ,because it goes only in the x direction.

We can assume that the second vector can be represented as: V₂=130cos(30°)i - 130sin(30°)j , this is 30° because the problem statement gives a 60° from the ground. Looking at it as a 90° triangle being made with the ground gives that the downward angle from the first vector it 30°.

The resultant is given by adding the given vectors: V₁ +V₂

V₁ +V₂ = R = (350+130cos(30°))i+(-130sin(30°))j

=> R = 462.583i - 65j

The magnitude of the resultant is given by:

|R| = radical[(R_x)²+(R_y)²]

=>|R| = radical[(462.583)²+(-65)²] = 462.128 ft