MEPV$102$ Practical Example $3\mathrm{.}7-$ Ball Trajectory

The height of a ball at any given time is given as:

$y(t)=y_0+V_{y0}t+\frac{1}{2}g{t}^2$

where

$y_0=$ Initial height of the object from the ground,

$V_{y0}=$ Initial vertical velocity of the object

$g=$ gravitational acceleration

The horizontal distance travelled by the ball as a function of time after it has been thrown:

$x(t)=x_0+V_{x0}t$

where

$x_0=$ Initial horizontal position of the ball on the ground,

$V_{x0}=$ Initial horizontal velocity of the ball

If the ball is thrown with an initial velocity $V_0,$ and at angle $,$ then the horizontal and vertical

components are:

$V_{x0}=V_0$Cos$$

$V_{y0}=V_0$Sin$$

Assume that the ball is initially thrown from a position $(x_0,y_0)=(0,0)$ with an initial velocity $V_0$ of $20$

metres per second at an initial angle of $$ degrees. Write a program that will plot the trajectory of

the ball and also determine the horizontal distance travelled before it touches the ground again. The

program should plot the trajectories of the ball for all angles $$ from $5$ to $85$ in steps of $10,$ and it

should determine the horizontal distance travelled for all angles $$ from $0$ to $90$ in steps of $1.$ Finally

it should determine the angle $$ that maximizes the range of the ball and plot that particular

trajectory in a different colour with a thicker line.