How to Calculate the Height of the Springboard
What is the equation representing the height of a diver above the water?
The equation h(t) = -4t² + 11t + 3 represents the height of a diver above the water in meters, t seconds after the diver leaves the springboard.
How can we determine the height of the springboard?
Show your work to calculate the height of the springboard.
Equation for Diver's Height:
The equation h(t) = -4t² + 11t + 3 represents the height of a diver above the water (in meters) at time t.
Calculating Springboard Height:
To calculate the height of the springboard, we need to find the initial height, which occurs at t=0. By substituting t=0 into the equation h(t) = -4t² + 11t + 3, we get:
h(0) = -4(0)² + 11(0) + 3 = 3 meters
Quadratic functions play a crucial role in determining the height of objects over time, such as in this case where we are calculating the height of a diver above the water. The given equation h(t) = -4t² + 11t + 3 allows us to track the diver's height as time progresses.
When dealing with finding the height of the springboard, it is essential to understand that the initial height corresponds to the time when the diver leaves the springboard, which is represented by t=0 in the equation. By substituting t=0 into the equation, we can determine that the springboard is 3 meters above the water.
Understanding the basics of quadratic functions and how to apply them in real-world scenarios, like calculating the height of objects, can be valuable in various fields such as physics, engineering, and mathematics.