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Question

Two particles having position vectors r=(3i+5j)m and r2=(5i+3j)m are moving with velocities V1=(4^i4^j)ms1 and V2=(a^i3^j)ms1 . If they collide after 2 seconds , the value of a is

A
-2
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B
-4
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C
-6
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D
-8
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Solution

The correct option is D -8
Let us consider the values as following:
r1=(3i+5j)mr2=(5i+3j)mv1=(4i4j)m/sandletv2be=(ai3j)m/st=2sec
If two particles collides after time "t" they travel equal distance.
r1+v1t=r2+v2t(3i+5j)+(4i4j)×2=5i+3j+(ai3j)2onsolvingweget,3i+8i+5j8j=5i+3j2ai6i11i+5i3j=2ai3j16i=2aia=162=8m/s2

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