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Question

Two particles are projected from the top of a tower with velocities 10 m/s and 80 m/s in horizontal but in opposite directions. After what time t their velocity vectors will be mutually perpendicular to each other? (Take g=10 m/s2)

A
22 sec
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B
2 sec
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C
8 sec
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D
4 sec
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Solution

The correct option is A 22 sec

Let u1 and u2 be the initial velocities of two particles projected from the top of the tower.
u1=80^i m/s and u2=10^i m/s

Let t be the time after which their velocity vectors are mutually perpendicular.
At time t, velocity of both the particles can be given by
v1=80^i(gt)^j and
v2=10^i(gt)^j

For the two velocity vectors to be perpendicular, we can write
v1.v2=0
(80^i(gt)^j).(10^i(gt)^j)=0
800+g2t2=0
t=8=22 sec

Hence option A is the correct answer

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