Use a computer to carry out the following step-by-step quantitative calculations for a baseball. Remember that the direction
of the air resistance force on an object is opposite to the direction of the object's velocity.
A baseball has a mass of 155 grams and a diameter of 7 cm. The drag coefficient C for a baseball is about 0.35, and the
density of air at sea level is about 1.3 × 10−3 grams/cm3, or 1.3 kg/m3.
(a) Including the effect of air resistance, compute and plot the trajectory of a baseball thrown or hit at an initial speed of
100 miles per hour, at an angle of 45 to the horizontal. How far does the ball go? Is this a reasonable distance?
(A baseball field is about 400 feet from home plate to the fence in center field. An outfielder cannot throw a baseball
in the air from the fence to home plate.)
(b) Plot a graph of (K + Ug) vs. time.
(c) Temporarily neglect air resistance (set C = 0 in your computations) and determine the range of the baseball. Check
your computations by using the analytical solution for motion of a projectile without air resistance. Compare your
result with the range found in part (a), where the effect of air resistance was taken into account. Is the effect of air
resistance significant? (The effect is surprisingly large—about a factor of 2!)
(d) Neglecting air resistance, plot a graph of (K + Ug) vs. time.
(e) In Denver, a mile above sea level, the air is about 83% as dense as the air at sea level. Including the effect of air
resistance, use your computer model to predict the trajectory and range of a baseball thrown in Denver. How does the
range compare with the range at sea level?