An object is released into the air at an height of 12ft and upward velocity of 30ft per second.
Write a function to model height h, in feet, of the object t seconds after it was released.


To model the height \( h \) of the object \( t \) seconds after it was released, you can use the following quadratic function derived from the principles of projectile motion:

\[
h(t) = -16t^2 + v_0 t + h_0
\]

Where:
- \( h(t) \) is the height in feet at time \( t \).
- \( v_0 \) is the initial upward velocity (30 ft/s).
- \( h_0 \) is the initial height (12 ft).
- The term \(-16t^2\) accounts for the effect of gravity (approximately \(32 \, \text{ft/s}^2\), hence divided by 2).

Substituting the values:

\[
h(t) = -16t^2 + 30t + 12
\]

This function gives the height of the object at any time \( t \) after it has been released. 

Would you like further details or have any questions? Here are some related questions for you to consider:

1. What is the maximum height the object reaches?
2. How long does it take for the object to hit the ground?
3. What is the height of the object after 1 second?
4. How does changing the initial velocity affect the height function?
5. What would happen if the object was thrown downward instead of upward? 

**Tip:** When modeling projectile motion, always remember to account for both the initial height and velocity in your function.

An object is released into the air at a height of 12ft and upward velocity of 30ft per second. Write a function to model height h, in feet, of the object t seconds after it was released.

Discover how to model the height of an object released from 12ft with an initial velocity of 30ft/s using the quadratic function h(t) = -16t^2 + 30t + 12. This page provides a comprehensive guide suitable for Grades 8-10 students exploring projectile motion concepts.

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