Question #4568

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

Expert's answer

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.

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.

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