0.3 A,B & C are three objects each ...
Question

# 0.3 A,B & C are three objects each moving with constant velocity. A's speed is 10 m/sec in a direction Po. The velocity ofB relative to A is 6 m/sec at an angle of, cos" (15/24) to PQ. The velocity of relative to B is 12 m/sec in a direction OP, then find the magnitude of the velocity ofC.

JEE/Engineering Exams
Physics
Solution
108
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( mathrm{v}_{mathrm{A}}=10 hat{mathrm{i}} ) ( mathrm{v}_{mathrm{B}}=6 cos alpha widehat{mathrm{i}}+6 sin alpha widehat{mathrm{j}} ) Here ( , cos alpha=frac{15}{24}, ) so ( sin alpha=frac{sqrt{351}}{24} ) ( mathrm{v}_{mathrm{CB}}=-12 widehat{mathrm{i}} ) ( mathrm{v}_{mathrm{BA}}=mathrm{v}_{mathrm{B}}-mathrm{v}_{mathrm{A}} ) ( 6 cos alpha widehat{mathrm{i}}+6 sin alpha widehat{mathrm{j}}=mathrm{v}_{mathrm{B}}-10 hat{mathrm{i}} ) or ( mathrm{v}_{mathrm{B}}=6 cos alpha widehat{mathrm{i}}+6 sin alpha widehat{mathrm{j}}+10 hat{mathrm{i}} ) ( =6 times frac{15}{24} widehat{mathrm{i}}+6 frac{sqrt{351}}{24} widehat{mathrm{j}}+10 widehat{mathrm{i}} ) ( =frac{55}{4} widehat{mathrm{i}}+frac{sqrt{351}}{4} widehat{mathrm{j}} ) But ( mathrm{v}_{mathrm{CB}}=mathrm{v}_{mathrm{C}}-mathrm{v}_{mathrm{B}} ) or ( mathrm{v}_{mathrm{C}}=mathrm{v}_{mathrm{CB}}+mathrm{v}_{mathrm{B}} ) ( =-12 widehat{mathrm{i}}+frac{55}{4} widehat{mathrm{i}}+frac{sqrt{351}}{4} widehat{mathrm{j}} ) ( =-frac{7}{4} hat{mathrm{i}}+frac{sqrt{351}}{4} widehat{mathrm{j}} ) or ( mathrm{v}_{mathrm{C}}=sqrt{left(frac{7}{4}right)^{2}+left(frac{sqrt{351}}{4}right)^{2}} ) ( =frac{20}{4}=5 mathrm{m} / mathrm{s} )