Mark hits a tennis ball into the air. He uses the equation shown to approximate the height, h, in feet, of the ball t seconds after he hits it.
h = -16t² + 88t + 4
What does the 4 represent in Mark’s equation?
The ball was in the air for a total of 4 seconds.
The ball landed 4 feet away from where Mark hit it.
The ball was 4 feet above the ground when Mark hit it.
The ball reached its maximum height 4 seconds after Mark hit it.
In Mark's equation, the constant term 4 represents the initial height of the ball. This means that the ball was 4 feet above the ground when Mark hit it.
To determine what the 4 represents in Mark's equation, we need to understand the equation itself. The equation given is h = -16t² + 88t + 4, which represents the height of the ball as a function of time.
The first term, -16t², represents the effect of gravity on the ball, causing it to decrease in height over time. The second term, 88t, represents the initial velocity of the ball, causing it to rise initially. The third term, 4, represents a constant value added to the equation.
Now, let's analyze the given answer choices:
1. The ball was in the air for a total of 4 seconds: This information is not directly related to the constant term 4 in the equation.
2. The ball landed 4 feet away from where Mark hit it: The constant term is not related to the distance the ball traveled horizontally. It only accounts for the vertical height of the ball.
3. The ball was 4 feet above the ground when Mark hit it: This choice is plausible, as the constant term 4 could represent the initial height of the ball when it was hit by Mark.
4. The ball reached its maximum height 4 seconds after Mark hit it: This choice is not related to the constant term in the equation, as the constant term represents a fixed value added throughout the ball's flight.
Based on the above analysis, the most plausible answer is that the constant term 4 represents the height of the ball above the ground when Mark hit it. Therefore, the answer is:
The ball was 4 feet above the ground when Mark hit it.