Question

An emergency helicopter is flying 1000 feet above the ground to drop water on a fire when the water is released. If its path through the air can be represented by the function h = -5.2t^2 + 1000, what is the helicopter's height (h) at time t?

A) h = -5.2t^2 + 1000
B) h = 1000 - 5.2t
C) h = -5.2t^2
D) h = 1000t^2 - 5.2

Answer 1

The helicopter's height at time t is given by the function A) h = -5.2t^2 + 1000, which shows a quadratic decrease in height as time increases, with an initial height of 1000 feet.

Step-by-step explanation:

The question asks us to determine the helicopter's height (h) at time t when represented by the function h = -5.2t^2 + 1000. This function shows the position of the helicopter as a function of time while considering the path of the water dropped is under the influence of gravity, similar to a projectile's motion.

The correct answer is A) h = -5.2t^2 + 1000, which indicates that as time passes, the height decreases quadratically due to gravity, starting from an initial height of 1000 feet. The coefficient -5.2 in front of t^2 represents the acceleration due to gravity, adjusted for the units of feet per second instead of meters per second, and the fact that the height is decreasing over time. None of the other options correctly represent the parabolic trajectory of the water's descent.