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

Answer:

4 seconds

Step-by-step explanation:

To solve this problem you will use the quadratic formula: $\frac{-b\pm\sqrt{b^2-4ac} }{2a}$.

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.

$\frac{-(32)\pm\sqrt{(32)^2-4(-16)(128)} }{2(-16)} \rightarrow \frac{-32\pm\sqrt{(1024)+(8192)} }{-32} \rightarrow \frac{-32\pm\sqrt{9216} }{-32} \rightarrow \frac{-32\pm96}{-32}$

Now split this into two equations.

$\frac{-32+96}{-32} ~and~\frac{-32-96}{-32}$

Positive case: $\frac{-32+96}{-32} \rightarrow \frac{64}{-32} =-2$

Negative case: $\frac{-32-96}{-32} \rightarrow \frac{-128}{-32} =4$

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