Two particles P and Q are projected simultaneously away from each other from a point A as shown in figure. The velocity of P relative to Q in `ms^(-1)` at the instant when the motion of P is horizontal is A. `10sqrt(4-sqrt3)`B. `20sqrt(4-sqrt3)`C. `10sqrt(4+sqrt3)`D. `20sqrt(4+sqrt3)`

Two particles P and Q are projected simultaneously away from each othe

1.	Two particles P and Q are projected simultaneously away from each other from a point A as shown in figure. The velocity of P relative to Q in `ms^(-1)` at the instant when the motion of P is horizontal is A. `10sqrt(4-sqrt3)`B. `20sqrt(4-sqrt3)`C. `10sqrt(4+sqrt3)`D. `20sqrt(4+sqrt3)`
Answer» Correct Answer - B b. Intially: `vecu_(P) = 20cos60hati + 20sin60^@hatj = 10hati + 10(sqrt3)hatj` `vecu = 20(sqrt2)[cos45^@(-hati)+sin45^@hatj] = -20hati + 20hatj` Initial relative velocity: `vec(u_(p//Q)) = vecu_(p)-vecu_(Q) = 30hati+(10(sqrt3)-20)hatj` `u_(p//Q) = sqrt(30^2+(10(sqrt3)-20)^2) = 20 sqrt(4-sqrt(3)) ms^(-1)` This relative velocity will remain same till both the particles are in air, because relative acceleration is zero.

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