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?

(1) h= 1/100 d² +75d+3
(2) h= 1/100 d² +75d-3
(3) h=- 1/100 d² +75d+3
(4) h=- 1/100 d² +75d-3

Answer 1

Option (3) h = -1/100 d² + 75d + 3 is the most realistic quadratic function to model the height of a javelin throw as it describes a parabolic trajectory where the javelin reaches a maximum height before descending.

Step-by-step explanation:

The question asks for a realistic quadratic function to model the height of a javelin above the ground in relation to the horizontal distance it has traveled.

Given that the height starts at a certain point above the ground and then reaches a maximum before coming back down, option (3) h = -1/100 d² + 75d + 3 is the most realistic function.

This is because the negative coefficient in front of the d² term indicates that the height reaches a maximum and then decreases, which is typical for the trajectory of a projectile, like a javelin throw.

The other functions would suggest that the javelin keeps ascending indefinitely or starts below the ground level, which are not physical scenarios.