The programmining language is Pyhton and I need fill in the balnks in the Starter code given below, but first this is info about the code:

Her cannon will shoot her at a velocity of 70m/s at a starting height of 5m . We will assume an acceleration of gravity g=9.8m/s^2 . We will simulate her trajectory for 10 seconds in 1,000 steps (so 1,001 states including the initial state.)

Angles

We will simulate 90 different angles from 190 . (Note: I misspoke in lecture on this point.) You will need to find the horizontal xx and vertical yy components of her initial velocity at each angle to simulate in two dimensions.

vx0=v0cos() , vy0=v0sin().

(Note that you will need to convert from degrees to radians before using the numpy sin and cos functions.)

Drag

To ensure Callista goes as far as possible, we cannot neglect drag in both the vertical and horizontal dimensions. To simplify things a bit, we will assume her surface area is equal in both dimensions. We will need to make use of the drag equation,

FD=12v2CDA.FD=12v2CDA.

Callista has a surface area of A=0.8m/s^2and a mass of mass=65kg . Her costume gives her a drag coeffienct of C_D . The mass density of the air is =1.225kg/m^3 . This force will always oppose her travel, so she will experience an acceleration of

adrag=*C_D*A*v^2/(2*mass)

(In other words, when she is ascending drag tends to slow her rise, and when she is descending drag tends to slow her fall. An if statement may be useful in implementing this.)

Remember that you will need to simulate this acceleration in both the xx and yy dimensions (both vertical and horizontal.) To simplify things a bit, compute this acceleration in the xx and y dimensions independently.

Simulation

When Callista hits the ground, she stops. To simulate this, if her altitude is ever less than 0, set her velocity in all directions to zero, her height to zero, and her x location to its previous value. Her x location should then remain the same until the end of the simulation. In other words, when she hits the ground, she stops moving until the 10 seconds we are simulating are over.

For each angle, you will need to simulate all 1,000 time steps. Each time you update the state variables, first compute her acceleration (using her previous speed to compute the drag,) then her velocity (using her current acceleration,) then her location (using her current velocity.)

Final answer

After the simulation is complete, we are not yet finished. Callista needs to know the optimum angle in integer degrees (being a cannonball not a mathematician).

((Starter Code: I need to fill in the ??? in the starter code and using your own code wont work for this at all )):

# 0. Place your necessary imports here. You may find it useful to be able to plot when debugging and visualizing your result. import numpy as np # 1. Create a 1D vector named `t` and 2D arrays named `vx`, `vy`, `x`, and `y` to hold the state variables, of size 90 x 1001. t = ??? # 2. Store the angles from 1 to 90 degrees as radians in a variable called `radians`. Use this to initialize the state variables for `vx` and `vy`. m = 90 # angles to fire at angles = ??? radians = angles * 2*np.pi/360 # 3. Define properties like gravity, Callista's surface area, and Callista's mass, and any other parameters you may need as they come up. A = 0.8 # m^2 g = 9.8 # m/s^2 # etc. Note that I expect an `initial_height` and `initial_velocity` below. # 4. At this point, you should have defined `t`, `x`, `y`, `vx`, `vy`, `radians`, and the properties you need. Now, initialize the starting condition in each array: for i in range(m): y[ i ][ 0 ] = initial_height vx[ i ][ 0 ] = initial_velocity * np.cos( radians[ i ] ) vy[ i ][ 0 ] = ??? # (see "Angles" above) # 5. Now you are ready to begin the simulation proper. You will need two loops, one over every angle, and one over every time step for that angle's launch. for i in ???: # loop over each angle for j in ???: # loop over each time step # check that the location isn't below the ground; if so, adjust as specified above # calculate the acceleration including drag # calculate the change in position at time `ts` using the current velocities (`vx[ i ][ j ]`) and the previous positions (`x[ i ][ j-1 ]`). This is slightly different from the previous example you solved in an earlier homework. # 6. The purpose of these calculations was to show which angle yielded the farthest distance. Find this out and store the result in a variable named `best_angle`.