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Applied Mechanics - Engineering

Q1:

A rod 5 m in length is moving in a vertical plane. When it is inclined at 60° to horizontal, its lower end is moving horizontally at 3 m/sec and upper end is moving in vertical direction. The velocity of its upper end, is

A 0.5 m/sec

B 1.0 m/sec

C 1.5 m/sec

D 2.5 m/sec

E 3.0 m/sec

ANS:B - 1.0 m/sec

The rod is moving in a way that it makes 60 angles with horizontal. It's rare, the end is moving horizontally with sqr 3 velocity which is the horizontal component of the resultant velocity. And the moving of the top end upward is a vertical component of the resultant velocity.

So, Let the resultant velocity is V, horizontal is Vh and Vertical is Vv and angle is ø,.
So, R cos ø = Vh,
R cos 60= sqr 3,
R= 3.46.

And R sin ø =Vv.
3.46 sin 60 = Vv
Vv= 3 m/s.