12.7: Exercises

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Before you go on, you might want to work on the following exercises.

Exercise 12.1

When the Boston Red Sox won the World Series in 2007, they played the Colorado Rockies at their home field in Denver, Colorado. Find an estimate of the density of air in the Mile High City. What effect does this have on drag? What effect does it have on the distance the baseball travels?

Exercise 12.2

The actual drag on a baseball is more complicated than what is captured by our simple model. In particular, the drag coefficient depends on velocity. You can get some of the details from Robert K. Adair’s The Physics of Baseball (Harper Perennial, 2002); the figure you need is reproduced at https://greenteapress.com/matlab/drag.

Use this data to specify a more realistic model of drag and modify your program to implement it. How big is the effect on the distance the baseball travels?

Exercise 12.3

According to Wikipedia, the record distance for a human cannonball is 59.05 m (see https://greenteapress.com/matlab/cannon).

Modify the example from this chapter to simulate the flight of a human cannonball. You might have to do some research to find the drag coefficient and cross-sectional area for a flying human.

Find the initial velocity (both magnitude and direction) you would need to break this record. You might have to experiment to find the optimal launch angle.

How much acceleration can a human withstand without injury? At this maximum acceleration, how long would the barrel of the cannon have to be to reach the initial velocity needed to break the record?