Question

A roller coaster travels 350 feet horizontally and then travels 130 feet at an angle of 60° from the ground what is a magnitude of the resultant vector ?

Answer 1

Before adding the vectors, we will write them in ordered pair notation.

The first vector is represented by the ordered pair:

`(350,0).`

The second vector is represented by the ordered pair:

`(130cos60^(\circ),130sin60^(\circ)),`

simplifying we get:

`(65,65√(3)).`

Adding the vectors, we get:

`(350,0)+(65,65√(3))=(415,65√(3)).`

Therefore, the magnitude of the resultant vector is:

`\sqrt{415^2+(65√(3))^2}.`

Simplifying the above result, we get:

`\sqrt{415^2+(65√(3))^2}=430.`

Answer:

`430.`