Question

You drive a car 660 ft to the east, then 370ft to the north. (a) What is the magnitude of your displacement? (b) Using a sketch, estimate the direction of your displacement (c) Verify your estimate in part (b) with a numerical calculation of the direction

Answer 1

a) 756.64 ft

b) 30 degrees

c) 29.27 degrees.

Step-by-step explanation:

We can represent the situation as follows:

So, we can find the magnitude of the displacement (the green line) using the Pythagorean theorem. Then:

`\sqrt[]{660^2+370^2}=\sqrt[]{435600+136900}=\sqrt[]{572500}=756.64\text{ ft}`

Then, the angle of the displacement can be approximate finding the angle θ. So, using a protractor on the figure, we get that θ is approximately 30 degrees.

Now, we can find the direction using a trigonometric function as:

`\tan \theta=(370)/(660)`

Because 370 is the opposite side and 660 is the adjacent side. Therefore, the value of θ is:

`\begin{gathered} \tan \theta=0.5606 \\ \theta=\tan ^(-1)(0.5606) \\ \theta=29.27\text{ degrees} \end{gathered}`

So, the answers are:

a) 756.64 ft

b) 30 degrees

c) 29.27 degrees.