Math Component

A cannonball is shot upward from the upper deck of a fort with an initial velocity of 192 feet per second.  The deck is 32 feet above the ground.

Use this formula to solve the problem:  h = -16t²+v₀t+h₀

Quadratic Model:  -16t²+192t+32

1.     How high does the cannonball go?    608 feet     (Remember you are looking for a specific part of the vertex.)

2.     How long is the cannonball in the air?   12.17 seconds  (Remember you can use the quadratic formula.)

Steps for finding th height:

·         Plug in our know units into the formula :

                h=-16t²+192t+32

·       Find the value of t. t represents time, use the formula t=     -b/(2a).

·         Now plug in the units from the equation above.

                t=(-192)/(2*-16)     Solve.

                t= 6 seconds

·         Now that you have the time, you can simply substitute it back into the original equation in the first step.

                  h=-16(6)²+192(6)+32  

                  h=-576+1152+32

                  h=608 feet.  

Steps for Finding the time in the air:

·         Plug in the known units into the formula:

                 h=-16t²+192t+32

·         Plug your units into the quadratic formula which is:

                            -b ±√b²-4ac  

                                     2a

·         Plug in our know units:                   -192±√(192)²-4(-16)(32)

2 (-16)

·         When you solve what is inside the square root symbol and you should end up with this:   

                                            -192±√38912

                                                    -32

·         Find the square root of what is in the inside the square root:

                                             -192 ± 197.3

                                                    -32

·         Now divide -32 into the top numbers and you recieve:

                                               6  ± -6.17

·         Since we are solving for time; you obviously can’t have a negative time, so you must solve for the answer which is positive. And that answer should be:

                                            t=12.17 seconds