Question

A ball is dropped from a 30-foot-tall building, meaning it has no initial velocity. Write a model h(t)
that represents the height of the ball from the ground, in feet, t seconds after it is dropped from the building.(2 points)
h(t)= t2+ t+

Answer 1

The model for the height of the ball, h(t), can be written as:

h(t) = -16t^2 + 30

Explanation:
The ball is dropped from a 30-foot-tall building, which means the initial height of the ball is 30 feet above the ground. The acceleration due to gravity causes the ball to fall downwards, so the equation for the height of the ball can be written as a quadratic function.

The standard form of a quadratic function is h(t) = at^2 + bt + c, where a, b, and c are constants. In this case, the coefficient of t^2 is -16 because the acceleration due to gravity is -32 feet per second squared. The initial velocity of the ball is zero, so the coefficient of t is also zero. The initial height of the ball is 30 feet, so the constant term c is 30.

Substituting these values into the quadratic function, the model for the height of the ball is:

h(t) = -16t^2 + 30