$2)$ Filenames: bounce$\_$mod.py

ENGR$103\_$HW$7\_2.$py

a$)$ Create a module, bounce$\_$mod.py$,$ in which you define a function that calculates the trajectory

of a bouncing ball.

Function syntax: x$,$ z$,$ t $=$ bounce$($v$0,$theta$0,$CR$,$N$,$dt$)$

v$0$: initial velocity of the ball $[$m$/$s$]$

theta$0$: angle of the initial velocity $[$deg$]$

CR: coefficient of restitution $-0<<=1.$ This is the ratio of vertical velocity

immediately after impact to the vertical velocity immediately before impact.

N: Number of impacts with the ground to include in the calculated trajectory

dt: time step $$ difference between adjacent points in the time vector, t

Your function will calculate the trajectory of the bouncing ball over N bounces. That is$,$ it will

calculate N trajectories, each of which is governed by the equations describing the motion of a

projectile.

$()=0$

$()=01$

$22$

What differs from one bounce to the next is the starting location, starting time, and initial

velocity.

The most challenging aspect of this assignment is accounting for the fact that each time and

location of impact does not, in general, correspond to a sampling interval. That is$,$ because you

are calculating only a discrete number of points along the trajectory, in general, the initial points

calculated for all but the first trajectory, and the final points calculated for all N trajectories, will

not be at $=0.$

b$)$ Write a second script, ENGR$103\_$HW$7\_2.$py$,$ in which you do the following

$$ Define the input parameters to be passed to bounce.py $($i$.$e$.,$ v$0,$ theta$0,$ CR$,$ n$,$ and

dt$).$

$$ Call bounce.py to calculate x$,$ z$,$ and t vectors for the trajectory of a bouncing ball.

$$ Plot the resulting trajectory $($z vs$.$ x$).$

The plot should look like the plot below and should have the following characteristics.

$$ Use plt$.$fill to create a gray $($RGB values: $[0\mathrm{.}6,0\mathrm{.}6,0\mathrm{.}6]$ ground plane, whose

thickness is $10\%$ of the maximum height of the entire trajectory.

$$ Set the x$-$axis limits to range from zero to the next integer beyond the last point of the

trajectory.

$$ Set the y$-$axis limits to range from the bottom of the gray ground area to $10\%$ beyond

the maximum height of the trajectory.

$$ The second line of the title should change according to the values of the parameters

passed to bounce.py$.$

You should experiment with a wide range of input parameters to verify that your function works

for all cases. When you submit your script, set the input parameters to: v$0=5,$ theta$0=50,$

CR$=0\mathrm{.}8,$ N$=10,$ and dt$=1$e$-3.$

Looking ahead to the next homework assignment, you will be using your bounce.py function to

create an animation of the bouncing ball