Question

1. a tennis ball is served from a height of 8 feet and just clears the net that is 3 feet high. the server is 40 feet from the net. if the ball travels in a straight path, how far on the other side of the net does the ball land?

Explanation:

Identify the geometric model

Using the Triangle Similarity knowledge point, we model the physical scenario using two nested right triangles that share a common acute angle at the landing point. The vertical segments representing the server's height (\(8\text{ ft}\)) and the net's height (\(3\text{ ft}\)) are both perpendicular to the ground, making them parallel.

Set up the similarity ratio

Using the Side Length Ratios knowledge point, the corresponding sides of these similar triangles are proportional. The smaller triangle has a vertical height of \(3\) and a horizontal base of \(x\). The larger triangle has a vertical height of \(8\) and a horizontal base of \(40 + x\).

Formulate the proportion

Using the Side Length Ratios knowledge point

$$ \frac{3}{x} = \frac{8}{40 + x} $$

Solve for the unknown distance

Using the Side Length Ratios knowledge point

$$
LATEXBLOCK0
$$

Answer:

\(24\text{ feet}\)