Math Component

Math Component

Use the quadratic model h = -16t²+v₀t+h₀ to solve the following problem:

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. 

First you have to plug in you the numbers in the equation.

t= time in feet per second

v= initial velocity

h=initial height

your new equation would be the following:

          h= -16t²+ (192)t+(32)

to find your vertex you use the formula –b/2a.

 –b= 192

a= -16

once you solve using this formula, your answer should have been 6.

Now you plug this number in the equation for t.

Your answer should result in height of 608 feet.

Now to find the time that the cannon ball was in the air, you use the quadratic formula.

-b±√b²-4ac

2a

a=-16

b=192
c=32

Plug in the numbers above into the corresponding formula to determine your zeros.

          Once you have plugged them in, solve for the negative

Which will result in (-.1644) second

Once you solve for the positive your answer will be 12. 16 seconds.

In this case our valid answer will be 12.16 seconds because time is only valid in positive form.