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+
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
To find the model h(t) that represents the height of the ball from the ground, we need to consider the effects of gravity.
Since the ball is dropped from a 30-foot-tall building, the initial height of the ball is 30 feet.
Additionally, we know that the acceleration of gravity is -32 ft/s^2 (negative since it acts downwards). So, the equation for the height of the ball as a function of time can be written as:
h(t) = -16t^2 + 0t + 30
Simplifying further, we have:
h(t) = -16t^2 + 30
Therefore, the model h(t) representing the height of the ball from the ground, in feet, t seconds after it's dropped from the building is h(t) = -16t^2 + 30.
To write a model h(t) that represents the height of the ball from the ground, we need to consider a few factors.
We know that the ball is dropped from a 30-foot-tall building and has no initial velocity. This means that the only force acting on the ball is gravity, causing it to fall straight downward.
In the absence of any other forces or factors like air resistance, the height of an object in free fall can be described by the following equation:
h(t) = 1/2 * g * t^2
In this equation, h(t) represents the height of the ball at time t, g represents the acceleration due to gravity (approximately 9.8 m/s^2 or 32 ft/s^2), and t represents the time in seconds.
Since we are given that the ball is dropped from a 30-foot-tall building, we need to adjust the model to account for this starting height.
So, the modified equation becomes:
h(t) = 30 - 1/2 * g * t^2
In this equation, 30 represents the initial height of the ball.
Therefore, the model h(t) that represents the height of the ball from the ground, in feet, t seconds after it is dropped from the building is:
h(t) = 30 - 1/2 * g * t^2