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Q.

A particle is projected from ground with a velocity of 40 m/s making an angle of 30o with horizontal. Then

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a

After 2 sec, its velocity vector will be perpendicular to the initial velocity vector.

b

After 3 sec, its velocity vector will be perpendicular to the initial velocitylk vector.

c

After 3.5 sec, its velocity vector will be perpendicular to the initial velcoity vector.

d

Velocity vector of the particle will never be perpendicular to the initial velocity vector.

answer is D.

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Detailed Solution

Velocity vector will be perpendicular to a the initial velocity vector if angle of projection is greater than 45o.Since u→ is perpendicular to V→,u→.v→=0i.e. ucosαi^+usinαj^.ucosαi^+usinα−gtj^=0⇒ t=ugsinαNow t>T⇒ugsinα>2usinαg⇒α<45o
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