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Two particles P and Q are projected simu...

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)`

Text Solution

Verified by Experts

The correct Answer is:
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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