PSAT Math Multiple-Choice Question 463: Answer and Explanation

Question: 463

The figure above shows the partial trajectory of a cannonball shot into the air. Assuming that the cannonball lands at a point where the height is 0, approximately how many feet farther did the cannonball travel horizontally than vertically upward? (1 yard = 3 feet)

• A. 335
• B. 425
• C. 935
• D. 1,390

Correct Answer: D

Explanation:

D

Difficulty: Hard

Getting to the Answer: Make sure you read the axis labels, the question, and the answer choices carefully. The vertical axis is labeled in feet, while the horizontal axis is labeled in yards. The answer choices are given in feet, so you'll need to convert the yards to feet.

The question asks for the difference between the horizontal and vertical distances the cannonball travels. You have a parabola-shaped graph, so sketch in a quadratic model, making sure to extend it past the last point all the way back to the x-axis.

Horizontally, the cannonball starts at 0 yards and travels to about 485 yards, or 485 × 3 = 1,455 feet. Determining vertical travel is a bit more involved. According to the graph, the cannonball's peak height is about 75 feet, but it started at 10 vertical feet (not 0), making the net upward distance traveled 65 feet. Subtract to find the difference, 1,455 - 65 = 1,390 feet, which is (D).

Note: Don't worry if you didn't draw the model exactly right or if you didn't get the exact same answer. The choices should be far enough apart that you'll still know which one is correct.