Asked by John
An automobile leaves the store, first going south at 88 km/h for 2 hours, and then turns on a road heading 20 degrees east of north at 55 km/h for 1.5 hours. Calculate the (x,y) components of the net displacement of the automobile from the starting position, where the x-axis is east and y-axis is north. Calculate the magnitude and direction of the automobile's net displacement. Give the magnitude in km and its direction using points of the compass.
Answers
Answered by
Henry
D1 = 88 * 2 = 176km, S.
D2 = 55 * 1.5 = 82.5km[70o] N. of E.
X = 82.5*Cos70 = 28.22 km.
Y = -176 + 82.5*sin70 = -98.5 km.
D = sqrt(X^2+Y^2) = sqrt(28.22^2+98.5^2) = 102.5 km.
Tan A = Y/X = (-98.5)/28.22 = -3.49043, A = -74o = 74o S. of E.
= Direction.
D2 = 55 * 1.5 = 82.5km[70o] N. of E.
X = 82.5*Cos70 = 28.22 km.
Y = -176 + 82.5*sin70 = -98.5 km.
D = sqrt(X^2+Y^2) = sqrt(28.22^2+98.5^2) = 102.5 km.
Tan A = Y/X = (-98.5)/28.22 = -3.49043, A = -74o = 74o S. of E.
= Direction.
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