Question

find a value of α such that velocities va=3i+6j and vb=2i+αj represent velocities of cars moving in same direction.
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Answer 1

answer . The velocity of a body A is xi^+6j^ m/s and the velocity of a body B is 3i^+2j^ m/s. Find the value of x such that the relative speed of A with respect to B becomes 5 m/s.

Velocity of A,A⃗ =xi^+6j^.

Velocity of B,B⃗ =3i^+2j^.

Velocity of A with respect to B is A⃗ −B⃗

⇒A⃗ −B⃗ =xi^+6j^−3i^−2j^=(x−3)i^+4j^ m/s.

It is given that the relative speed of A with respect to B is 5 m/s.

⇒∣∣A⃗ −B⃗ ∣∣=5⇒∣∣(x−3)i^+4j^∣∣=5.

⇒(x−3)2+16=25⇒x2−6x=0.

⇒x(x−6)=0⇒x=0 or x=6.