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Homework Statement
An ant with a velocity of 20mm/s [W] crawls on a stick that is being dragged [W25 N] at 50mm/s. what is the velocity of the ant relative to the ground?
Homework Equations
Let A = ant, Let S=stick, Let G=ground, Let N and W be positive. Vag=?, Vas=20mm/s [W], Vsg=50mm/s[W25N]
The Attempt at a Solution
Vag=Vas + Vsg
Vas = Vasx + Vasy
= 20mm/s + 0mm/s
Vsgx = Vsg(cos25)
=50mm/s(cos25)
=45.315 mm/s
Vsgy= Vsg(sin25)
=50mm/s(sin25)
=21.130mm/s
Vagx=Vasx +Vsgx
=20mm/s+45.315mm/s
=65.3mm/s
Vagy= Vasy + Vsgy
= 0mm/s +21.130mm/s
=21.1mm/s
V2ag=V2agx +V2agy
Vag= (65.3mm/s)2+(21.1mm/s)2 - This is square root as well
Vag=68.6mm/s
Tan@= O/A
@= Tan-1(21.1mm/s / 65.3mm/s)
@= 17.9
@=18
Therefore the Ant s velocity relative to the ground is 68.6mm/s [W18N]