Question

A decathlete at the Olympics throws a javelin such that its height, h, above the ground can be modeled as a quadratic function of the horizontal distance, d, that it has traveled. Which of the following is a realistic quadratic function for this scenario?

(a) 1/100 d² + 75d + 3
(b) 1/100 d² + 75d - 3
(c) -1/100 d² + 75d + 3
(d) -1/100 d² + 75d - 3

Answer 1

The realistic function modeling the height of a thrown javelin is (c) -1/100 d² + 75d + 3, as it correctly represents the parabolic trajectory with a maximum point followed by a decrease in height. Therefore, the correct answer is option (c) -1/100 d² + 75d + 3.

Step-by-step explanation:

The realistic quadratic function for the scenario where a decathlete throws a javelin and its height, h, above the ground is modeled as a function of the horizontal distance, d, would typically be one where the squared term is negative. This is because the height of the javelin will increase to a maximum point and then decrease, forming a parabolic trajectory. The correct option that represents this trajectory is (c) -1/100 d² + 75d + 3. This function indicates that the height will increase as the javelin is thrown, reach a maximum height, and then decrease as it falls back to the ground, which is consistent with the physics of projectile motion.