Chapter 6.4, Problem 65E

Applying What You’ve Learned

A dangerous tradition. In this exercise we will investigate the dangerous practice that some have of firing a gun into the air at midnight on New Year’s Eve. Assume that someone fires a gun straight up and that the bullet reaches a height of one-half mile (a mile is 5,280 feet).

a. Use the information given in Exercise 63 to determine how long it will take the bullet to hit the ground. (See disclaimer below.*)

*This is what w e call a “textbook exercise” and we are ignoring very important factors such as air resistance and spin on the bullet. In a 2006 episode of MythBusters, they neither confirmed nor denied that a falling bullet alone could be fatal. Nonetheless, firing weapons into the air does cause fatalities, probably due to the fact that the weapon is usually not fired straight up into the air and hence the bullet maintains much of its original velocity from being fired.

b. Assuming that an object that falls for $t$ seconds will hit the ground at a speed of $32t$ feet per second, find the speed of the bullet in feet per second when it hits the ground.

c. Convert feet per second to feet per hour and then divide by $5,280$ to find the speed of the bullet in miles per hour.