Question
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after aunch, x in seconds, by the given equation. Using this equation, find the maximum height eached by the rocket, to the nearest tenth of a foot.
Ask by Johnston West. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
To find the maximum height of the rocket, you need to provide the specific equation relating height \( y \) to time \( x \). Once you have the equation, follow these steps:
1. **Identify the Equation:** Ensure it's in the form \( y = ax^2 + bx + c \).
2. **Find the Vertex:** Use the formula \( x = -\frac{b}{2a} \) to determine the time at which the maximum height occurs.
3. **Calculate Maximum Height:** Substitute the \( x \) value back into the equation to find \( y \).
**Example:**
If the equation is \( y = -16x^2 + 64x + 80 \), the maximum height is **144.0 feet**.
Please provide the specific equation for an accurate calculation.
Solution
It looks like the equation relating the rocket's height \( y \) to the time \( x \) after launch wasn't provided. To determine the maximum height reached by the rocket, the specific form of the equation is essential. Typically, such equations are quadratic (of the form \( y = ax^2 + bx + c \)), where the maximum height can be found by analyzing the vertex of the parabola.
**Here's what you can do:**
1. **Provide the Equation:** If you have the specific equation, please share it so I can help you calculate the maximum height accurately.
2. **General Approach (If the Equation is Quadratic):**
- **Standard Form:** Assume \( y = ax^2 + bx + c \).
- **Vertex Formula:** The time at which the maximum height occurs is \( x = -\frac{b}{2a} \).
- **Maximum Height:** Substitute this \( x \) value back into the equation to find \( y \).
**Example:**
Suppose the height equation is \( y = -16x^2 + 64x + 80 \).
1. **Find the Time at Maximum Height:**
\[
x = -\frac{b}{2a} = -\frac{64}{2(-16)} = 2 \text{ seconds}
\]
2. **Calculate the Maximum Height:**
\[
y = -16(2)^2 + 64(2) + 80 = -64 + 128 + 80 = 144 \text{ feet}
\]
So, the rocket reaches a maximum height of **144.0 feet**.
Please provide the specific equation if you need a precise calculation!
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To find the maximum height reached by the rocket, you can use the vertex formula for a quadratic equation of the form \( y = ax^2 + bx + c \). The x-coordinate of the vertex, which gives the time at maximum height, is found using the formula \( x = -\frac{b}{2a} \). Once you find this time, substitute it back into the equation to get the maximum height \( y \). Don't forget to double-check your calculations! A common mistake is miscalculating the coefficients or forgetting to square the time when substituting back into the height equation. Keep your formulas handy and perhaps work with a partner to spot any oversight!
