Two bodies move in a straight line towards each other at initial velocities `v_(1)` and `v_(2)` and with constant acceleration `a_(1)` and `a_(2)` directed against the corresponding velocities at the initial instant. What must be the maximum initial separation between the bodies for which they meet during the motion ?

Options

A. `(v_(1)^(2))/(a_(1)) + (v_(2)^(2))/(a_(2))`
B. `((v_(1) + v_(2))^(2))/(2(a_(1) + a_(2)))`
C. `(v_(1)v_(2))/(sqrt(a_(1)a_(2)))`
D. `(v_(1)^(2) - v_(2)^(2))/((a_(1) - a_(2)))`

Answer

B

Explanation

`v_("rel") = v_(1) + v_(2)`
`a_("rel") = (a_(1) + a_(2))`, directed oppposite to motion.
Using, `v^(2) - u^(2) = 2 as`, we have
`(0)^(2) - (v_(1) + v_(2))^(2) = - 2 (a_(1) + a_(2))s`
`s = ((v_(1) + v_(2))^(2))/(2(a_(1) + a_(2)))`