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?

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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.