**Our next contest is:**

*April 17, 2018*

**Cannonball Trajectory**

Anyone who has observed a
baseball in motion (or, for that matter any other object thrown into the air)
has observed projectile motion. The ball
moves in a curved path and its motion is simple to analyze if two assumptions
are made: the free fall acceleration is constant over the range of motion and
is directed downward, and the effect of air resistance is negligible. With these assumptions made, it was found
that the path of a projectile or its trajectory is always a parabola.

When calculating the path of
a projectile, it is important to keep track of the height of the
projectile. Back during the civil war
there were no computers to do this for the army, and when a cannonball was
launched, the angle of elevation was simply estimated. Your job is to help the army by constructing
a graph of a cannonball during its flight, when given the angle of elevation
and the velocity at which it will travel.

The path that a projectile
takes once it has been launched can be modeled with the following equations (given
by Sir Issac Newton):

X=V * T * COS(A)

Y=(V * T * SIN(A))-(0.5 * G * (T^{2}))

**Where**

X = horizontal distance the projectile has traveled

Y = height of the projectile

A = the angle of degrees above the horizon

G = acceleration due to gravity (9.8 meters/s^{2} on earth)

T = the number of seconds into the flight we are interested in

V = velocity of the projectile

Using the above equations,
for any given T, we can compute how high (Y) the projectile will be and how far
down range (X) the projectile will be.

The cannon has
4 notches of elevation:

Notch 1: 30 degrees

Notch 2: 45 degrees

Notch 3: 60 degrees

Notch 4: 70 degrees

Your
program will input 2 numbers, the notch number and velocity and then print a
horizontal bar graph that plots the cannonball's height every time X increases
by 50 meters. For example, it might look like this:

50 ****

100 *********

150 ************

200 *****************

250 *********************

300 *****************

350 ************

400 *********

450 ****

Where each
star represents 10 meters of height (Y). Since Y will not always come out an even multiple of 10, you should
round up to the next even multiple of 10 (15 would be 2 stars). You should
continue to plot until the height becomes negative which means that the cannonball
has hit the ground. If Y does not become negative when X has reached 1000
meters, then you should stop plotting anyway.

In order to plot the path you
will need to use the built in **SIN** and **COS****SIN** or **COS** (180 degrees = pi radians, 90 degrees = pi/2
radians, etc).

For our purposes, we will use
pi = 3.14159.

Input:

The input file will contain a
list of numbers, one on each line. The
first number corresponds to the notch of the cannon, and the second number
corresponds to the velocity. Input
should be read until the notch and velocity are both
zero, indicating the end of input.

Output:

X distances should be right
justified, so that 50 lines up with 1000.
There should be one space between the distance and the first star. There should be a blank line between each set
of output. There should not be a blank
line at the end of the output.