Objective: Apply the bisection method to find the time it takes for a falling object to reach the ground, given its initial height.

Problem Description: Consider an object falling from an initial height $(0)$ according to the kinematic equation:

$($t$)=0-1/2$gt$^2$

$($t$)$ is the height of the object at time t$,$

$0$ is the inital height,

g is the acceleration due to gravity $($approximately $9\mathrm{.}8$ m$/$s$^2),$

t is the time.

Tasks:

$1.$ Implement the height$\_$equation function in Python to represent the height equation of the falling object.

$2.$ Implement the bisection$\_$method$\_$for$\_$falling$\_$object function to find the time it takes for the object to reach the ground using the bisection method. Use a maximum of $100$ iterations and a desired tolerance of $1106.$

$3.$ Test your implementation with an initial height of $50$ meters.

$4.$ Explore the effect of changing the initial height on the time it takes for the object to fall. Try at least two different initial heights.