Question

Two particles P and Q are moving with constant velocities (î+j^) and (-î+j^) respectively. At time t=0, P is at origin and Q is at a position vector (2î+j^). Find the equation of path Q with respect to P.

Answer 1

velocity of P , v = i + j

initial position of particle P is origin.

so, position of particle after time t , S = vt

= (i + j)t ....(1)

velocity of particle Q , v'= -i + j

initial position of particle Q = (2i + j)

so, position of particle Q after time t , S' = (2i + j) + v't

= (2i + j) + (-i + j)t .....(2)

now equation of path Q with respect to P = S' - S

= (2i + j) + (-i + j)t - (i + j)t

= 2i + j - 2t i

= (2 - 2t)i + j This is required equation.