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quicksilver123
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Homework Statement
A ladybug with a velocity of 10.0mm/s [W] crawls on a chair that is being pulled [50deg N of W] at 40.0mm/s. What is the velocity of the ladybug, relative to the ground?
Homework Equations
pythag theorum
component vectors
sohcahtoa
The Attempt at a Solution
Let [N] and [W] be positive.
Velocity of the ladybug relative to the chair = VLC = 10mm/s [W]
Components:
VLCx = 10mm/s
VLCy = 0mm/s
Velocity of the chair, relative to the ground = VCG = 40mm/s [W50degN]
Components:
VCGx = 40mm/s (cos50) = 25.71150439mm/s
VCGy = 40mm/s (sin50) = 30.64177772mm/s
Velocity of the ladybug, relative to the ground = VLG = ?
Components:
VLGx = VLCx + VCGx = 35.71150439mm/s
VLGy = VLCy + VCGy = 30.64177772mm/s
Direction of VLG
∅ (theta?) = tan-1(opposite/adjacent)
= tan-1(VLGy / VLGx)
= tan-1(30.64177772mm/s / 35.71150439mm/s)
= 40.63 degrees
∴ VLG = √2214.230088 = 47.05560634mm/s [ W 40.63deg N ]I feel that my calculations are correct.
However, looking up this question on the net shows that people have come to a different end result:
https://www.physicsforums.com/showthread.php?t=596229
Specifically, the direction of the resultant vector is different.
I just want to be sure that my answer is correct before I submit it for marking.
Thanks.
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