Question

Greg drives 10 km north from his home to get to school. After class he drive 7 km west to grab some dinner. With reference to his home where is the restaurant?

Answer 1

Given data:

* The distance traveled by Greg towards the north is d_1 = 10 km.

* The distance traveled by Greg towards the west is d_2 = 7 km.

Solution:

The displacement of Greg from the home to the restaurant is,

`D=\sqrt[]{d^2_1+d^2_2}`

Substituting the known values,

`\begin{gathered} D=\sqrt[]{10^2+7^2} \\ D=\sqrt[]{100+49} \\ D=\sqrt[]{149} \\ D=12.2\text{ km} \end{gathered}`

Thus, the restaurant is at the displacement of 12.2 km from the home.

The direction of the restaurant is,

`\begin{gathered} \tan (\theta)=(10)/(7) \\ \tan (\theta)=1.43 \\ \theta=55^(\circ) \end{gathered}`

Thus, the restaurant from home is north of the west direction making an angle of 55 degrees with the west.