When a projectile is launched at an angle $\backslash$theta to the horizontal with an initial velocity V$,$ its

motion can be described by the following equations $($where the angle is measured in radians$)$:

$-$ Maximum height $($H$)=($V$2*$ sin$2(\backslash$theta $))/(2*$ g$),$ where g is the acceleration due to gravity

$($approximately $9\mathrm{.}81$ m$/$s$^2$ on Earth$).$

$-$ Total flight time $($T$)=(2*$ V $*$ sin$(\backslash$theta $))/$ g$.$

$-$ Horizontal range $($R$)=($V$2*$ sin$(2*\backslash$theta $))/$ g$.$

Write a JAVA program that asks the user for the initial velocity and launch angle. Validate that the

initial velocity is positive and that the angle is between $0$ and $90($loop until these are valid$).$

Then calculate and print the three values above.

NOTE: use Java constants for g $=9\mathrm{.}81$ and for the conversion from degrees to radians which is

equal to $0\mathrm{.}0174533.$ To calculate a sin in Java, use Math.sin$($x$)$ and to square a value, use either

x$*$x or Math.pow$($x$,2).$ sin$2(\backslash$theta $)$ is the same as sin$(\backslash$theta $)*$ sin$(\backslash$theta $).$

Limit output to one decimal $($see sample output$)$

SAMPLE OUTPUT:

Welcome to the Projectile Motion Calculator!

Enter the initial velocity $($in meters per second$)$: $-20$

Initial velocity must be a positive value.

Enter the initial velocity $($in meters per second$)$: $30$

Enter the launch angle $($in degrees$)$: $110$

Launch angle must be between $0$ and $90$ degrees.

Enter the launch angle $($in degrees$)$: $-2$

Launch angle must be between $0$ and $90$ degrees.

Enter the launch angle $($in degrees$)$: $45$

Results:

Maximum height: $23$ meters maximum height

Total flight time: $4\mathrm{.}3$ seconds

Horizontal range: $91\mathrm{.}8$ meters