Math Component

Quadratic Model h= -16t²+v₀t+h₀

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. 

Quadratic Model: __________________

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

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

Step to solve first problem:You use the formula-   b/2a

Step 1:I used the -b over 2a for the first equation.

Step 2:The b term is 192 which is my velocity and I put a negative outside of the parentheses.

Step3:I put negative 192 over 2 times my a term which is -16 .

Step3:The I put negative 192 over -32 which the answer is 6.

Step 4: Then I plugged all the numbers in the t  -16(6)^2+192+32 .

Step 5:That gives me the answer of 608 ft.

Steps to solve Second Problem

Step1:I use the Quadratic Formula which is  negative b Plus or minus square root b squared negative 4 ac over two a.

Step 2 :I plug my numbers in the right places in the quadratic formula.

Step 3:I put negative 192 in the -b outside of the square root.

Step 4:I insert a plus and minus before the square root .

Step 5: plug in 192^2 in the b squared area and then minus 4 and times (-16) because that represents a and multiply the c represents 32.

Step 6:I put a dividing symbol and put 2 times-16. Negative 192 plus and minus square root of 38912 divided by negative 32.

Step 7:I plugged each number in twice for instance negative 192 minus the square root divided by negative 32 and negative 192 plus the square root and divided by negative 32.

Step8: I came up with the answer and that is two diffrent answers negative.16 and 12.16. I go with the highest number which is 12.16 because the question is asking how long does the cannonball go up in the air.