A balloon is ascending at the rate of `9.8ms^(-1)` at a height of 39.2m above the ground when a food packet is dropped from the balloon. After how much time and with what velocity does it reach the ground? Take `g=9.8ms^(-2)` .

Explanation

Initially the food packet attains the upward velocity of the balloon, so
`u=9.8ms^(-1),g=9.8ms^(-2),s=-39.2m`
Here s is taken negative because it is in the opposite direction of initial velocity.
using, `s=ut+1/2"gt"^2` we get
or `4.9t^2-9.8t-39.2=0` or `t^2-2t-8=0`
or `(t-4)(t+2)=0` or `t=4s or -2s`
As time is never negative, so t = 4s. Velocity with which the food packet reaches the ground is
`v=u+"gt"=9.8xx4=-29.4ms^(-1)`
Negative sign shows that the velocity is directed vertically downwards.