This problem has two parts: the first part (the most important part) is solving the final nonlinear equation in the problem statement for .

Once is known, you can this solve for the location of the football, i.e., solve for and using a series (or vector) of time values. I used numpy.linspace() function to create a time vector and then solved for and at each time point, i.e.,

time = numpy.linspace(0,4)

x = x0 + v0*math.cos(theta)*time

y = y0 + v0*math.sin(theta)*time – (g*time**2)/2.0

Then, you can generate an vs. plot showing the trajectory of the ball. If the ball doesn’t reach the target or if the ball goes through the ground (i.e., negative values for ) then you know that you choose a range of time values that is too short or too long. If you’ve watched much (American) football, then you know that the ball is typically in the air for a few (more than 1 and less than 5 seconds) even for long throws.

Please make sure to include the input code and output as well as the memo. Please do it in your own work and words. Thanks

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