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A stick of length 100 cm rests against a vertical wall and the horiziontal floor. If the foot of the stick slides with constant velocity of 10 cm/s then find the magnitude of velocity of middle point of stick when inclined at 30° with floor.

A stick of length 100 cm rests against a vertical wall and the horiziontal floor. If the foot of the stick slides with constant velocity of 10 cm/s then find the magnitude of velocity of middle point of stick when inclined at 30° with floor.

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1 Answers

Vikas TU
14149 Points
4 years ago
Dear student 
Let M is midpoint , and coordinate of midpoint is (x,y) 
x = L/2 CosQ 
y = L/2 SinQ 
Q is angle of inclination .
dx/dt = L/2 d(CosQ)/dt
dy/dt = L/2 d(SinQ)/dt 
d/dt(LcosQ) = 10
L(-sinQ)dQ/dt = 10 
-sinQ  dQ/dt = 10/100 = 00.1
dQ/dt = -0.1 CosecQ 
|Vm| = sqrt(Vmx^2 + Vmy^2) 
= L/2 (dQ/dt) 
50 *|-0.1CosecQ|
= 5CosecQ
= 5Cosec30 = 10 cm/sec
Good Luck 
   

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