Answer to Question #4568 in Mechanics | Relativity for Theresa

Question

if you leave your home and drive at a speed of 55 mph for 1.5 hours 60 degrees North of East, then 40 mph for 3 hours 10 degrees East of North, what is your net displacement from home? give your answer in miles with an angle

Answer 1

Let's calculate the displacement along the axis East-West and the axis South-North.
East-West: 55*1.5*cos(60deg)-40*3*sin(10deg) = 20.41 miles.
South-North: 55*1.5*sin(60deg)+40*3*cos(10deg) = 189.62 miles.

The total displacement is sqrt(20.41^2+189.62^2) = 190.72 miles
and the angle is atan(189.62/20.41) = 83.86 degrees North East.