Question

In the following exercises, solve. The distance an object falls varies directly to the square of the time it falls. A ball falls 72 feet in 3 seconds, (a) Write the equation that relates the distance to the time. (b) How far will the ball have fallen in 8 seconds?

Name: Problem 482, Chapter 8: Elementary Algebra
Uploaded: 2021-07-26T19:12:59-08:00
Duration: 1 min 37 s
Channel: Teresa Fuston
Description: In the following exercises, solve. The distance an object falls varies directly to the square of the time it falls. A ball falls 72 feet in 3 seconds, (a) Write the equation that relates the distance to the time. (b) How far will the ball have fallen in 8 seconds?

   In the following exercises, solve.
The distance an object falls varies directly to the square of the time it falls. A ball falls 72 feet in 3 seconds,
(a) Write the equation that relates the distance to the time.
(b) How far will the ball have fallen in 8 seconds?

Elementary Algebra

Lynn Marecek 2nd Edition

Chapter 8, Problem 482

Instant Answer

Solved by Expert Teresa Fuston

07/26/2021

Step 1

This can be written as an equation of the form \(Y = kX^2\), where \(Y\) is the distance, \(X\) is the time, and \(k\) is the constant of variation. Show more…

Show all steps

Thanks for your feedback!

In the following exercises, solve. The distance an object falls varies directly to the square of the time it falls. A ball falls 72 feet in 3 seconds, (a) Write the equation that relates the distance to the time. (b) How far will the ball have fallen in 8 seconds?

Play audio

Feedback

Teresa Fuston and 79 other educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Proportionality Constant

The proportionality constant is a fixed number that relates two variables in a direct or quadratic variation. It can be determined by substituting known values into the equation and solving for the constant, which then allows the prediction of other values within the relationship.

Direct Variation

Direct variation describes a relationship between two variables in which one variable is a constant multiple of the other. In this type of relationship, if one variable increases, the other increases proportionally, and the equation can be expressed in the form y = kx where k is the constant of proportionality.

Quadratic Relationship

A quadratic relationship occurs when one variable is proportional to the square of another variable. This is often seen in physical situations like free-fall motion where the distance covered is proportional to the square of the time elapsed, leading to an equation of the form d = kt².

Please give Ace some feedback