Math Practice: Cannon Edition!

For problems concerning velocity, we learned that the correct formula to use is

h = -16t²+v₀t+h₀

The formula translates to this when you add in the variables for height and velocity. 192 ft/sec is the velocity, 32 feet is the height.  

h= -16t²+192t+32

I plugged the formula into my graphing calculator and then I went to the table to find the maximum height that it goes on the y-axis. In this case, the maxium height was 608 feet.

Then, to find how long the cannonball is in the air, you plug the a, b, and c values into the quadratic formula, which is this:

-b ±√(b²-4ac)/2a



With the variables plugged in, the formula now looks something like this.

-192±√((192)²-4(-16)(32))/2(-16)

When you plug this into your calculator, the answer comes out to be about 12 seconds in the air.