Question

The function h(t)=-16t2+32t+128 represents the height of a cnnoj ball in feet t seconds after it is shot from a cannon. How many seconds does it take the cannonball to hot its target on thr grownd

Answer 1

4 seconds

Explanation:

To solve this problem you will use the quadratic formula:
`(-b\pm√(b^2-4ac) )/(2a)`.

Identify the a, b, and c values of the given quadratic equation:

• a = -16
• b = 32
• c = 128

Substitute these values into the quadratic formula.

`(-(32)\pm√((32)^2-4(-16)(128)) )/(2(-16)) \rightarrow (-32\pm√((1024)+(8192)) )/(-32) \rightarrow (-32\pm√(9216) )/(-32) \rightarrow (-32\pm96)/(-32)`

Now split this into two equations.

`(-32+96)/(-32) ~and~(-32-96)/(-32)`

Positive case:
`(-32+96)/(-32) \rightarrow (64)/(-32) =-2`

Negative case:
`(-32-96)/(-32) \rightarrow (-128)/(-32) =4`

Since time cannot be negative, the cannonball takes 4 seconds to hit its target on the ground.