Question 1119141
Anna runs 4 meters 40 degrees North of East, then 2 meters East, then 5.2 meters 30 degrees South of West. And finally 6.5 meters south before stopping for water break. Find her resultant displacement from where she started?
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Label the points A, B, C, D & E in order.
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For AB:
x = 4*cos(40), y = 4*sin(40)
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For BC:
x = 2, y = 0
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For CD:
x = -5.2*sin(60), y = -5.2*cos(60)
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For DE:
x = 0, y = -6.5
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Add them.
x = 4cos(40) + 2 - 5.2*sin(60) = 4cos(40) - 5.2*sin(60) + 2 =~ 0.5608
y = 4sin(40) - 5.2*cos(60) - 6.5 =~ -6.5288
Point E is (0.5608,-6.5288)
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AE = sqrt(x^2 + y^2) = ~6.5529 meters from start
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I'm sure she needs water after running 17.7 meters, = 58 feet.