IIT JEE , AIEEE Forum - Physics , Mechanics - tuf problem in kinematics.....try this one

ganesha1991

Two rods of equal length are lying one along x-axis and other along line y=x.
they intersect at origin at their midpoint . The first rod moves with velocity v₁= vj
and the second with velocity v₂ = v /

2 i - v /

2j . Find the velocity of point of intersection of two rods?

answer will be given later.................ok i'lll give it now itself...............
it is v ( 2.41i+j )

anchitsaini

edit!

ganesha1991

gud attempt....................close enuf anchit

prash_shan_jpr

I m getting it as

(2-root2)v as magnitude

savvej

let rod 1 displace upwards by y1
let rod 2 displace rightwards by x2 and downwards by y2
now we have eqn of rod 1 (ie.the line) as y=y1
and of rod 2 as y=x+(y2-x2)
solveig them to get pt of intersection ,we get
y=y1
and x= y1-y2 +x2
dx/dt will give me velocity of pt of intersection in x direction
and dy/dt will give velocity of pt of intersection in y direction
.:dy/dt=dy1/dt
=v
dx/dt=v-(-v/root2)+v/root2
=2.14v
now v vector = dx/dt i + dy/dt j
= 2.14v i + vj
= v(2.14i+j)

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