Project ForgeA rigid link PQ is 2 m long and oriented at 20° to the horizontal, with Q at the upper-left end and P at the lower-right end. The velocity VQ = 1 m/s is directed at 45° from the vertical at Q, and the velocity VP at P is directed horizontally (along the line of the 20° angle shown at P). The magnitude of VP (in m/s) at this instant is
- A2.14
- B1.89
- C1.21
- 0.96
Explanation
For any rigid link, the velocity components of its two end points RESOLVED ALONG THE LINK must be equal (otherwise the link would stretch). Link direction (P→Q) is 20° above horizontal, i.e. at 160° from the +x axis. VQ is at 135° from the +x axis (45° from vertical), giving an angle of 25° between VQ and the link, so VQ's component along the link = 1×cos25°≈0.9063 m/s. VP is horizontal (180° from +x axis), giving an angle of 20° between VP and the link. Setting components equal: VP·cos20° = 0.9063, so VP = 0.9063/cos20° ≈ 0.9063/0.9397 ≈ 0.96 m/s.
Source: GATE ME 2014 (Session 1 / Set-1) (2014)
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