**The equation** y=−16⁢t2+V⁢t+H **represents the height of a toy rocket, in feet, above the ground after being launched from a platform** H **feet above the ground, where** t **is the time, in seconds, after the toy rocket is launched, and** V **is its initial velocity, in feet per second. If the toy rocket is launched from a platform that is** 5 **feet above the ground and has an initial velocity of** 80 **feet per second, which equation represents the height of the toy rocket above the ground?** 

We are given the general equation for the height of a toy rocket:

\[
y = -16t^2 + Vt + H
\]

Where:
- \( y \) represents the height of the rocket in feet above the ground.
- \( t \) represents the time in seconds after the rocket is launched.
- \( V \) is the initial velocity in feet per second.
- \( H \) is the height of the platform (initial height above the ground) in feet.

### Given:
- The rocket is launched from a platform 5 feet above the ground, so \( H = 5 \).
- The initial velocity of the rocket is 80 feet per second, so \( V = 80 \).

### Substituting these values into the equation:
\[
y = -16t^2 + 80t + 5
\]

This equation represents the height of the toy rocket above the ground after \( t \) seconds.

### Final equation:
\[
y = -16t^2 + 80t + 5
\]

This is the required equation for the height of the toy rocket.

Would you like more details on how this equation models the rocket's motion?

---

Here are 5 related questions you might consider:

1. How does the term \(-16t^2\) represent the effect of gravity on the rocket's height?
2. What is the significance of the initial velocity \( V \) in the equation?
3. How would the equation change if the initial velocity were different?
4. At what time \( t \) does the rocket reach its maximum height?
5. How can we find out when the rocket hits the ground using this equation?

**Tip:** The term \(-16t^2\) comes from the effect of gravity on the object. In feet per second squared, the acceleration due to gravity is approximately \(-32 \text{ ft/s}^2\), but this is halved in the equation because it's a constant of integration from physics equations.

The equation y = -16t^2 + Vt + H represents the height of a toy rocket, in feet, above the ground after being launched from a platform H feet above the ground, where t is the time, in seconds, after the toy rocket is launched, and V is its initial velocity, in feet per second. If the toy rocket is launched from a platform that is 5 feet above the ground and has an initial velocity of 80 feet per second, which equation represents the height of the toy rocket above the ground?

Learn how to derive the height equation y = -16t^2 + 80t + 5 for a toy rocket launched with an initial velocity of 80 feet per second from a platform 5 feet above the ground. This problem covers quadratic equations and the effects of gravity on projectile motion, suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation