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?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! 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.
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