A body is projected up such that its position vector varies with time as `vecr={3thati+(2t-t^(2))hatj} m`. Here `t` is in second.The time when its `y`-coordinate is zero is

Answer

(i)zero (ii) right (iii) `0.2 m` (iv) `2.2 m` (v) `1.8 m`

Explanation

(i) CM does not shift
(ii) Plank moves towards right.
(iii) `Deltax_(cm) = (m_(1)Deltax_(1) + m_(2)Deltax_(2) + M Deltax)/(m_(1) + m_(2) + M) = 0`
`rArr 0 = (50(x + 2) + 70(x - 2) + 80x)/(50 + 70 + 80)`
`rArr x = 0.2m` (right)
(iv) `Deltax_(m_(1)) = x + 2 = 2.2 m` (right)
(v) `Deltax_(m_(2)) = x - 2 = -1.8m` (rleft)