An object is falling towards the ground according to the equation [tex]h(t) = 245 - 5t^2[/tex], where [tex]t[/tex] is measured in seconds and [tex]h(t)[/tex] is measured in meters.

What is the height of the object at time [tex]t[/tex]?

A) [tex]245 - 5t^2[/tex]
B) [tex]5t^2 - 245[/tex]
C) [tex]245 + t^2[/tex]
D) [tex]5t^2 + 245[/tex]

The correct form of the height equation of an object falling towards the ground at time t is A) 245-5t². This quadratic equation accurately represents how the height of the object changes as it falls, considering the initial height and the effect of gravity over time.

Explanation:

The question concerns the equation of motion for an object falling towards the ground, specifically asking for the correct form of the height equation at time t. The correct answer is given by the option A) 245-5t2, which represents the height h(t) of the object at any given time t.

This equation is a quadratic equation in time which shows how the height of an object changes over time as it falls towards the ground, factoring in the acceleration due to gravity. In the provided equation, 245 meters is the initial height from which the object is dropped, and -5t2 represents the distance fallen over time, assuming a simplified gravitational acceleration factor.