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[9.06] Jacob kicks a soccer ball off the ground and in the air with an initial velocity of 33 feet per second. Using the formula H(t) = −16t2 + vt + s, what is the maximum height the soccer ball reaches?


15.1 feet


16.5 feet


17.0 feet


18.2 feet

Verified Answer :

H[33/22] = - 16 (33/32)^2 + (33/32)33  + 0

= approximately 17.0 feet

Hope this helps

Answer:

C. 17.0 feet

Step-by-step explanation:

We have been given that Jacob kicks a soccer ball off the ground and in the air with an initial velocity of 33 feet per second. We are asked to find the maximum height the soccer ball using formula \(H(t)=-16t^2+vt+s\).

First of all, we will substitute \(v=33\) in our given formula.

\(H(t)=-16t^2+33t+0\)

Since our given parabola has a negative leading coefficient, so it will be downward opening parabola. The maximum height of the ball will be y-coordinate of the vertex of parabola.

Let us find x-coordinate of parabola as:

\(\frac{-b}{2a}=\frac{-33}{2\times -16}=\frac{-33}{-32}=\frac{33}{32}\)

Now, we will substitute \(x=\frac{33}{32}\) in our formula to find y-coordinate of vertex.

\(H(\frac{33}{32})=-16(\frac{33}{32})^2+33(\frac{33}{32})+0\)

\(H(\frac{33}{32})=-16*\frac{1089}{1024}+\frac{1089}{32}\)

\(H(\frac{33}{32})=-16*1.0634765625+34.03125\)

\(H(\frac{33}{32})=-17.015625+34.03125\)

\(H(\frac{33}{32})=17.015625\)

\(H(\frac{33}{32})\approx 17.0\)

Therefore, the ball reached the maximum height of 17.0 feet and option C is the correct choice.