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Question

A cannon ball is fired with a velocity 200 m/sec at an angle of 60 with the horizontal. At the highest point of its flight it explodes into 3 equal fragments, one going vertically upwards with a velocity 100 m/sec, the second one falling vertically downwards with a velocity 100 m/sec. The third fragment will be moving with a velocity


A

100 m/s in the horizontal direction

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B

300 m/s in the horizontal direction

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C

300 m/s in a direction making an angle of 60° with the horizontal

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D

200 m/s in a direction making an angle of 60° with the horizontal

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Solution

The correct option is B

300 m/s in the horizontal direction


Momentum of ball (mass m) before explosion at the highest point = mvi=mu cos 60^i

=m×200×12^i=100 m^i kgms1

Let the velocity of third part after explosion is V

After explosion momentum of system =

P1+P2+P3

=m3×100^jm3×100^j+m3×V^i

By comparing momentum of system before and after the explosion

m3×100^jm3×100^j+m3V^i=100m^iV=300m/s


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