Chapter 9.3, Problem 8STP

A ball is dropped from the top of a building that is 250 feet tall. The height h of the ball in feet after t seconds is modeled by the function $h=-16t^2+250$

h = 1612 + 250. Round to the nearest tenth if necessary.

a. How long will it take for the ball to reach the ground? Show your work.

b. How long will it take for the ball to reach a height of 75 feet? Show your work.

To determine

To calculate: The time taken the ball to reach the ground.

Answer to Problem 8STP

The time taken the ball to reach the ground $=3.95\text{ sec}$ .

Explanation of Solution

Given information: A ball is dropped from the top of a building that is $250$ feet tall. The height h of the ball in feet after t seconds is modelled by the function $h=-16t^2+250$ .

Calculation:

A ball is dropped from the top of a building that is $250$ feet tall. The height h of the ball in feet after t seconds is modelled by the function $h=-16t^2+250$ .

The time taken the ball to reach the ground when $h=0$ .

  $\begin{array}{l}0=-16t^2+250\\ t^2=\frac{250}{16}\\ t=3.95\text{ sec}\end{array}$

To determine

To calculate: The time taken the ball to reach a height of $\text{75 feet}$

  $=3.3\text{ sec}$ .

Answer to Problem 8STP

The time taken the ball to reach the ground $=3.95\text{ sec}$ .

Explanation of Solution

Given information: A ball is dropped from the top of a building that is $250$ feet tall. The height h of the ball in feet after t seconds is modelled by the function $h=-16t^2+250$ .

Calculation:

A ball is dropped from the top of a building that is $250$ feet tall. The height h of the ball in feet after t seconds is modelled by the function $h=-16t^2+250$ .

The time taken the ball to reach the ground when $h=75$ .

  $\begin{array}{l}75=-16t^2+250\\ t^2=\frac{175}{16}\\ t=3.3\text{ sec}\end{array}$