The distance an object falls varies directly to the square...

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?

Key Concepts

Equation Setup Using Provided Data

Setting up the equation involves establishing the form of the relationship (in this case, distance equals the constant times the square of time) and then substituting known values to solve for the constant. This approach exemplifies how to use specific data points to create a general equation that can predict other outcomes in similar situations.

Quadratic Relationship

A quadratic relationship occurs when one variable depends on the square of another one. In this context, the distance fallen is dependent on the square of the time, which means the math involves squaring the time value and then multiplying by the constant of proportionality.

Direct Variation

Direct variation is a relationship between two quantities where one quantity is a constant multiple of the other. In problems like this, the distance falls directly as the square of time, meaning that as time increases, the distance increases proportionally to the square of that time, with a constant factor determining the exact amounts.

Constant of Proportionality

The constant of proportionality is the factor that relates the two varying quantities in a direct variation. It is determined by substituting known values into the relationship equation and solving for the constant. Once found, it can be used to compute unknown values by maintaining the same proportional relationship.

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