Q$1-$ If $n$ is the number of iterations of the loop, use a count$-$controlled loop as the basis for

the algorithm. $($a$)$ Develop an algorithm and, $($b$)$ write an example of the pseudocode for the

parachutist problem. Recal:

Equation $(1\mathrm{.}10$ is a model that relates the acceleration of a falling object to the forces act$-$

ing on it$.$ It is a differential equarion because it is written in terms of the differential rate of

change $(d\frac{v}{d}r)$ of the variable that we are interested in predicting. Howover, in contrast to

the isolution of Newton's second law in Eq$.$ The exact solution of Eq$.(1\mathrm{.}10$ for the ve$-$

locity of the falling parachutist cannot be obtained uxing simple algobraic manipulation.

Rather, more advanced techniques such as those of calculus, must be applied to obtain an

exact or analytical solution. For example, if the parnchutist is initially at rest at

$x=0,$ calculus can be used to solve Eq$.(1\mathrm{.}10$ for

$v(r)=\frac{gm}{c}(1-e^{-(e)mar})$

Note that Eq$.(1\mathrm{.}10)$ is cast in the general form of Eq$.$ where $v(t)-$ the depen$-$

dent variable, $t=$ the independent variable, $c$ and $m=$ parameters, and $g=$ the forcing

runction.

The approach in the foregoing example can be employed to develop an algorithm for

the parachutist problem. Recall that, given an initial condition for time and velocity, the

problem involved iteratively solving the formula

$v_{i+1}=v_i+\frac{d{v}_i}{dt}t$