Two billiard balls are rolling on a flat table. One has velocity components vx=1m/s, vy=3m/s and other has components ,vx′=2m/s and vy′=2m/s.. If both the balls start moving from the same point, the angle between their Paths is

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60°

45°

22.5°

15°

answer is D.

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Detailed Solution

v1=1i+3j and v2=2i+2jv1⋅v2=(i+3j)⋅(2i+2j)=2+23or v1v2cos⁡θ=2+23cos⁡θ=12×12+32×12=cos⁡60cos⁡45+sin⁡60sin⁡45=cos⁡(60−45)=cos⁡15or θ=15∘