Question

A hot-air balloon is ascending at the rate of 12 m/s and is 80 m above the ground when a package is dropped over the side. (a) How long does the package take to reach the ground? (b) With what speed does it hit the ground?

Answer 1

Answer:

Explanation:

Given

balloon is ascending at the rate of $u=12\ m/s$

Balloon is at a height of $s=80\ m$

As the package is dropped from the balloon it must possess the same initial velocity as the balloon

using

$v^2-u^2=2as$  

where v=final velocity

u=initial velocity

a=acceleration

s=displacement

$v^2=12^2+2\times 9.8\times 80$

$v^2=1712$

$v=41.37\ m/s$

time taken is  given by

$v=u+at$

substituting values

$41.37=-12+9.8\times t$

as we consider downward direction as positive

$t=\frac{53.37}{9.8}$

$t=5.44\ s$

therefore time taken to reach the bottom is t=5.44 s