Chapter 1.9, Problem 13Q

Solution

To find: The function with height $h$ (in feet).

  $2.029$ seconds

Given information:

The ball through upward at height 5 feet with vertical velocity of 30 feet per second.

Calculations:

The path of ball is parabolic. Let the path equation be $h=-\frac{1}{2}g{t}^2+v_{0}t+h_0$

Initial height of the ball is, $h_o=5$

Initial velocity, $v_o=30$

Gravity, $g=32$

Substitute the value into the model,

  $\begin{array}{l}h=-\frac{1}{2}\left(32\right)t^2+30t+5\\ h=-16t^2+30t+5\end{array}$

The model the path is $h=-16t^2+30t+5$ .

Since the ball hit the ground, the height of the ball is 0.

  $\begin{array}{c}-16t^2+30t+5=0\\ t=-0.154,2.029\end{array}$

Since time cannot be negative, the time of flight of the ball is 2.029 seconds.