Chapter SH, Problem 9.5EP

(a)

To determine

To find: The height of the ball after one second if the equation of the height is $h=-16t^2+60t$ .

Answer to Problem 9.5EP

The height of the ball is 44 feet after one second.

Explanation of Solution

Given information:

The given equation of the height is $h=-16t^2+60t$ and the time is $t$ .

Calculation:

To calculate the height after one second, substitute 1 for $t$ in the equation.

  $\begin{array}{c}h=-16{\left(1\right)}^2+60\left(1\right)\\ =-16+60\\ =44\text{feet}\end{array}$

Therefore, the height of the ball is 44 feet after one second.

(b)

To determine

To find: The time when the ball will reaches to a maximum height.

Answer to Problem 9.5EP

The ball will reaches to a maximum height at $1.875$ seconds.

Explanation of Solution

Given information:

The given equation of the height is $h=-16t^2+60t$ and the time is $t$ .

Calculation:

To calculate the time when the ball reaches to a maximum height, find the vertex and the x -coordinate represents the time.

Compare the given equation with the standard quadratic $y=a{x}^2+bx+c$ .

  $a=-16,b=60,c=0$

Determine the equation for the axis of the symmetry.

  $x=\frac{-b}{2a}$

Substitute 60 for $b$ and $-16$ for $a$ .

  $\begin{array}{c}x=\frac{-60}{2\left(-16\right)}\\ =\frac{60}{32}\\ =1.875\end{array}$

Therefore, the ball will reaches to a maximum height at $1.875$ seconds.

(c)

To determine

To find: The time when the ball will hit the ground.

Answer to Problem 9.5EP

The ball will hit the ground after $3.75$ seconds.

Explanation of Solution

Given information:

The given equation of the height is $h=-16t^2+60t$ and the time is $t$ .

Calculation:

When the ball hit the ground, the height will be zero. To calculate the time when the ball hit the ground, substitute 0 for $h$ in the equation.

  $\begin{array}{c}0=-16t^2+60t\\ 16t^2-60t=0\\ t\left(16t-60\right)=0\end{array}$

Solve the above equation for $t$ .

  $\begin{array}{c}t=0\\ t=3.75\end{array}$

From the above, the zero value of the time represents when it is kicked. Therefore, ball will hit the ground after $3.75$ seconds.