physics question

Question

A family drives 63.6 miles west and 11.2 miles south. What is their resultant

displacement?

Select one:

a. 64 miles @ 24° south of west

b. 128 miles @ 24 ° south of west

c. 128 miles @ 10 ° south of west

d. 64 miles @ 10 ° south of west

Answer 1

We can get the total distance from the Pythagorean theorem: a^2 + b^2 = c^2

Plugging in the numbers for west and south, we get a hypotenuse of 64 miles.

Next we can use some trig to get the angle--specifically we want SOH-CAH-TOA with the opposite and adjacent sides (south is opposite, west is adjacent).

tan(angle) = 11.2 / 63.6

so angle = arctan(11.2 / 63.6) = 10 degrees.