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+
30
To find the model h(t) that represents the height of the ball from the ground, we need to consider the equation for the motion of a freely falling object.
The equation for the height of the ball from the ground, h(t), can be represented as:
h(t) = -16t^2 + 30
In this equation, -16t^2 represents the effect of gravity, where 16 is half the acceleration due to gravity (32 ft/s^2) and t^2 represents the time squared. The term +30 accounts for the initial height of the ball from the ground, which is 30 feet.
Combining these terms, we get the complete model for h(t):
h(t) = -16t^2 + 30
To find the model h(t) that represents the height of the ball from the ground, we need to consider the motion of the ball.
When the ball is dropped, it experiences constant acceleration due to gravity. The distance fallen by an object under constant acceleration can be represented by the equation:
h(t) = (1/2) * g * t^2
Where:
h(t) is the height of the ball from the ground at time t
g is the acceleration due to gravity (approximately 32.2 ft/s^2)
t is the time in seconds
Since the ball is dropped from a 30-foot-tall building, we need to take into account this initial height as well. Therefore, the final model for the height of the ball from the ground can be represented as:
h(t) = 30 - (1/2) * g * t^2