A1EN0502.doc - MathChamber

Direct Variation
A rubber ball is dropped out a window. The height that the ball bounces varies
directly with the height of that window. This relation is modeled by the
equation y = 0.4x, in which x represents the height from which the ball is
dropped in meters and y represents the height the ball bounces in meters.
1. The ball is dropped from a height of 25 m above the ground. How high does it
2. The ball bounces 13.5 cm in the air. From what height was it dropped?
3. List at least three factors other than starting height that could affect the final height
of the ball.
4. How might each of these factors change the equation? Would the new equation be
a direct variation? If so, come up with a new constant of variation that makes
sense given the factor(s) you have identified, and answer Exercises 1 and 2 for
your new direct variation.
5. Draw the graph of the original ball. Graph at least one of your new functions on
the same set of axes.
6. What can you say regarding the largest possible value for the constant of
variation given the situation described? Why does this limit exist? (What
would happen if the limit didn’t exist?)
7. The original rubber ball is dropped from the same distance, but hits the roof of a
building 20 ft of the ground. Is the resulting function still a direct variation?
Prentice Hall Algebra 1 • Teaching Resources
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