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Question

Trajectory of two particles projected from origin with speeds v1 and v2 at angles θ1 and θ2 with positive x-axis respectively are as shown in the figure. Given that g=10 m/s2(^j). Choose the correct option(s) related to diagram.


A
v1v2=2v1
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B
θ2θ1=2θ1
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C
v1=v2
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D
3(θ2θ1)=+θ1
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Solution

The correct option is D 3(θ2θ1)=+θ1
Given that,
Initial speeds of two particles are v1 and v2, angles of projection are θ1 and θ2 respectively.
From the figure, we can deduce that
Maximum height of particle1 (H1)=v21sin2θ12g
10=v21sin2θ12g .........(1)
Range of particle1 (R1)=v21sin2θ1g
40=v21sin2θ1g ........(2)
From (1) and (2) we get

14=sinθ14cosθ1tanθ14=14

tanθ1=1θ1=45

Substituting this in equation (2), we get, v21=400v1=20 m/s

Similarly, for second particle,

Maximum height of particle2 (H2)=v22sin2θ22g
15=v22sin2θ22g .........(3)
Range of particle2 (R2)=v22sin2θ2g
203=v22sin2θ2g .......(4)

From (3) and (4) we get

34=sinθ24cosθ2tanθ2=3θ2=60

Substituting this in (3) we get,

15=v22×sin2602×10

v22=400v2=20 m/s

Therefore, we can conclude that, v1=v2 and 3(θ2θ1)=+θ1.
Options (c) and (d) are correct.

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