What is the equation representing the height above the river at a given horizontal distance for a motorcycle stunt rider who jumps across the river?
The equation HH(x) = -0.0003x^2 + 2.19x + 400 represents the height above the river at a given horizontal distance for a motorcycle stunt rider. This equation allows us to calculate the height at various horizontal distances from the launch ramp. To better understand the path of the motorcycle rider, we can sketch and label a picture of the rider's path.
Sketching the Rider's Path
To sketch and label a picture of the rider's path, follow these steps:
1. Draw a horizontal line to represent the river.
2. On one end of the line, draw a vertical line to represent the bluff overlooking the river. Label it as "Bluff."
3. From the top of the bluff, draw a curved line sloping downwards towards the river. This curve represents the path of the motorcycle as it jumps across the river.
4. Label the curve as "Motorcycle Path."
5. On the curve, mark the point where the motorcycle lands on the level with the river. Label it as "Landing Point."
6. Mark the horizontal distance from the launch ramp on the curve and label it as "Distance."
7. Indicate the height above the river for certain distances along the curve. For example, mark the height at a distance of 150 feet above the river.
By following these steps, you can visualize the trajectory of the motorcycle stunt rider as she jumps across the river, starting from the bluff overlooking the river and landing on a level with the river. The equation HH(x) = -0.0003x^2 + 2.19x + 400 helps us understand how the height above the river changes with horizontal distance. It's a thrilling feat captured in a mathematical representation.