Question

A helicopter is ascending vertically witha speed of 5.40 m/s. At a height of 105 m above the earth a package is dropped from the helicopter. How much time does is take for the package to reach the ground

Answer 1

Answer: 5.21 s

Step-by-step explanation:

Given

Helicopter ascends vertically with
`u=5.4\ m/s`

Height of helicopter
`h=105\ m`

When the package leaves the helicopter, it will have the same vertical velocity

Using equation of motion

`\Rightarrow h=ut+(1)/(2)at^2\\\\\Rightarrow 105=-5.4t+0.5* 9.8t^2\\\Rightarrow 4.9t^2-5.4t-105=0\\\\\Rightarrow t=(5.4\pm √(5.4^2+4* 4.9* 105))/(2* 4.9)\\\\\Rightarrow t=(5.4\pm 45.68)/(9.8)\\\\\Rightarrow t=5.21\ s\quad \text{Neglect negative value}`

So, package will take 5.21 s to reach the ground