Assignment 2

Name:
Student #:

Q1

a)

A projectile is launched into the air with a firing angle of 37° over flat terrain.  The projectile is cleverly designed so that it experiences a quadratic drag force in the horizontal (x) direction of  -0.01 (Subscript[v, x])|v|, were v is the projectile’s velocity and (Subscript[v, x]) is the x-component of its velocity, while in the vertical (y) direction, it experiences a lift force of 0.4 (Subscript[v, x]) (assuming (Subscript[v, x]) is positive).  Assume the mass of the projectile to be 1.2 kg, its initial speed to be 35 m/s and acceleration due to gravity of 9.8m/s/s.

Plot the trajectory of the projectile.

How far horizontally does the projectile travel before hitting the ground?

b)

Write a function that takes as an argument the firing angle and returns the range of the projectile (horizontal distance travelled by the time it hits the ground).  Assume all other parameters are the same as in part (a).  [Note that the function Range[ ] already is a built-in function in Mathematica, so use a different name.]  Confirm that your function gives the same range for 37 Degree as in part (a).

(c)

Use your function from part (b) along with the Table[ ] function to creat a list of ordered pairs giving θ (in degrees) and the resulting range.  Use value of θ between 10 and 50 Degree in steps of 0.5.  Use ListPlot to plot the data (include axes labels).

(d)

Using the table you created in part (c), plot a subset of the data using only values of θ between (and including) 15 and 30 degrees.  Estimate the optimal firing angle.  Considering the following example will help you carry out this task.

list=Table[{i,i^2},{i,0,5,0.25}]

ListPlot[list]

list[[8;;15]]

ListPlot[list[[8;;15]]]

(e)

Interpolate your data from part (c) and use FindMaximum to find the optimal firing angle.  Evaluate the range at the optimal angle (use your function from part (b)).