Question

A weather balloon, rising vertically at 25.0 m/s, releases an instrument package when it is 100. meters above the ground. How many seconds does it take from when the package was released for the package to hit the ground?

Answer 1

7.74 seconds

Step-by-step explanation:

u = 25 m/s

h = - 100 m

Let it takes time t to hit the ground.

Use second equation of motion

`h = ut-(1)/(2)gt^(2)`

`-100 = 25t-4.9t^(2)`

`4.9t^(2)-25t-100=0`

`t=(25\pm √(625+4* 4.9* 100))/(2*4.9)`

`t=(25\pm 50.84)/(9.8)`

Take positive sign as time can never be negative.

t = 7.74 s

Thus, the package takes 7.74 seconds to reach the ground.