Question

Mr. McNiven is hiking in a Florida state park. If McNiven hikes 15 kilometers in a westerly direction, then turns 90 degrees and walks 30 kilometers directly south, determine the magnitude and direction McNiven is from his starting point.

Answer 1

33.5 km at
`63.4^(\circ)` south of west

Step-by-step explanation:

To solve the problem, we take the following convention:

- West is positive x-direction

- South is positive y-direction

Using this convention, we can describe the two parts of the motion as follows:

1) 15 km west: the components of this part of the motion are

`a_x = 15 km\\a_y = 0`

2) 30 km south: the components of this part of the motion are

`b_x = 0\\b_y = 30 km`

Therefore, the components of the net displacement are

`r_x = a_x + b_x = 15 + 0 = 15 km\\r_y = a_y + b_y = 0 +30 = 30 km`

So, the magntidue of the net displacement is

`r=√(r_x^2+r_y^2)=√(15^2+30^2)=33.5 km`

while the direction is:

`\theta=tan^(-1)((r_y)/(r_x))=tan^(-1)((30)/(15))=63.4^(\circ)`

south of west.