Problem $1$

Let's consider a physical model describing the velocity of a falling object subject to the forces of gravity and wind drag:

$\frac{\text{d}\text{e}\text{l}\text{v}(t)}{\text{d}\text{e}\text{l}\text{t}}=g-\frac{c_d}{m}v(t{)}^2,$

tin$(0,T)$

$v(0)=0.$

Create a $.$py file $($this will be added to the final submitted source file called

HW$1.$py$)$ and add a function called exact$\_$velocity$()$ that takes the following arguments as input in this order:

float $c_d$ : drag coefficient

float $m$ : the mass of the objects

vector$($float$)t$ : a vector of times the us$$r wants to compute the velocity at

float $g$ : gravitational constant

And returns the following output:

vector$($float$)v$ : the velocity at times from the input vector $t$ according to the equation of the exact solution to the model, $v(t)=\sqrt[\phantom{2}]{\frac{gm}{c_d}}tanh(\sqrt[\phantom{2}]{\frac{gcd}{m}}t)$

Hints: The input vector $t$ should assumed to be a numpy array. You are welcome to use the numpy $tanh()$ and sqrt$()$ functions.