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Q.

A particle A is projected from the ground with an initial velocity of 10 m/s at an angle of 60o with horizontal as shown in fig. (4). From what height hshould an another particle B be projected horizontally with velocity 5 m/s so that both the particles collide in ground at point C if both are projected simultaneously ?(g = 10 m/s2)

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a

10 m

b

30 m

c

15 m

d

25 m

answer is C.

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Detailed Solution

The horizontal component of velocity is given byucos⁡θ=10×cos⁡60∘=10×(1/2)=5m/sThis is same as the velocity of B in horizontal direction. Both wilt collide at C if their times of flights are equal, i.e., TA = TB2usin⁡θg=2hg ∵h=12gTB2∴ h2=2u2sin2⁡θg=2×(10)2(3/2)210=15m
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