Question

Two bodies move in a straight line towards each other at initial velocities v1 and v2 and with constant acceleration a1 and 2 directed against the corresponding velocities at the initial instant.The maximum initial separation between the bodies for which they meet during the motion is ______?

Answer 1

here's what i thought of till now:
let the initial separation be x. suppose in time t, body b1 covers a distance of y. so if bi and b2 have to meet, then in same time t, b2 should cover distance x-y.
so we get 2 eqs as,
y = v1t - 1/2 a1 t^2
x-y = -v2 t + 1/2 a2 t^2
adding these two,
x = (v1 - v2)t + 1/2( a2 - a1) t^2
now we need to find a way to eliminate t.

is this the right approach?

Answer 2

out of mind:)
hats off

Answer 3

my mind*

Answer 4

:) well, we need to do 2 things now. first, eliminate t. second, find out how to pitch in the 'max separation' factor.

Answer 5

Isn't the acceleration acting in opp. direction?

Answer 6

yup. it is. a1 is opp to v1 and a2 is opp to v2.

Answer 7

second.

Answer 8

so a1 and v2 are in the same dir - left.
and a2 and v1 are in same dir - right.

Answer 9

got it?

Answer 10

got the diag

Answer 11

@maheshmeghwal9 a1 should be opp to v1. same with v2 and a2

Answer 12

so i take back my words.

Answer 13

hmm. well, now that 'that' is cleared up, how do we eliminate t?

Answer 14

@DLS what's the answer given as?