Chapter 1.1, Problem 51E

a.

To determine

To identify: The type of function that models the height of the basketball.

Answer to Problem 51E

Function’s type is quadratic.

Explanation of Solution

Given Information: Function is $f(t)=-16t^2+32t+5.2$ .

  $f$ is a quadratic function.

Thus, the height of the basketball is modeled by a quadratic function.

b.

To determine

The value of $t$ when the ball is released from the hand.

Answer to Problem 51E

  $t=0$ when the ball is released from hand.

Explanation of Solution

Given Information: Function is $f(t)=-16t^2+32t+5.2$ .

At that point, the value of $t$ is $0$ because it is the time when ball just enters into the air and has no contact with the hand. Ball is at the most initial stage of its trajectory.

Thus, $t=0$ when the ball is released from hand.

c.

To determine

To calculate: The height of the ball above the ground when it is released from the hand.

Answer to Problem 51E

The height of the ball when it is just released from the hand is $5.2feet$ .

Explanation of Solution

Given Information: Function is $f(t)=-16t^2+32t+5.2$ .

Calculation:

Putting $t=0$ in the given function,

  $\begin{array}{l}$ f(0)=-16{(0)}^2+32(0)+5.2$\\ =5.2\end{array}$

Thus, the height of the ball when it is just released from the hand is $5.2feet$ .