Question

A balloon is going upwards with a velocity of $12m/s$. It releases a packet when it is at a height of $65m$ from the ground. How much time will the packet take to reach the ground if $g=10m/s^2$?

Answer 1

Step 1: Given Data

Since the balloon is going upwards against the gravity, the initial velocity is $u=-12m/s$

Height from which packet is released $h=65m$

Final velocity $v=0$

Acceleration due to gravity $g=10m/s^2$

Step 2: Formula Used

According to Newton's second law of motion

$S=ut+\frac{1}{2}a{t}^2$

$\Rightarrow h=ut+\frac{1}{2}g{t}^2$

$\Rightarrow 2h=2ut+g{t}^2$

$\Rightarrow g{t}^2+2ut-2h=0$

Step 3: Calculate the time taken

Upon substituting the values we get,

$10t^2+2\times \left(-12\right)t-2\left(65\right)=0$

$\Rightarrow 5t^2-12t-65=0$

$\Rightarrow 5t^2-5t+13t-65=0$

$\Rightarrow 5t\left(t-5\right)+13\left(t-5\right)=0$

$\Rightarrow \left(t-5\right)\left(5t+13\right)=0$

$\Rightarrow t=5,-\frac{13}{5}$

Since time cannot be negative,

$t=5s$

Hence, the time the package will take to reach the ground is $5s$.