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Q.

A particle is projected with speed 25 m/s at angle 53o from horizontal in front of an inclined plane mirror as shown in figure. Choose the correct option(s) (g = 10 m/s2).

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a

Speed of image w.r.t. object will be maximum after time 4 sec of projection.

b

Minimum speed of image w.r.t. object is zero.

c

Speed of image w.r.t. object will be minimum after time 7/8 sec of projection.

d

Maximum speed of image w.r.t. object is 50 m/s.

answer is A.

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Detailed Solution

Relative speed will be minimum (zero) when velocity of object will be parallel to plane mirror. tan⁡α=usin⁡θ−gtucos⁡θ⇒34=25⋅45−10t25⋅35⇒ 34=20−10t15⇒45=80−40t⇒ 40t=35⇒t=78sAt maximum relative speed, the object moves normal to mirror. And it occurs when the particle hits the ground. Hence, maximum relative speed = 50 m/s
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