Understanding the Physics
* Gravity: The primary force acting on the rocket is gravity, which causes it to slow down as it ascends. The acceleration due to gravity is approximately -32 feet per second squared.
* Initial Velocity: The rocket starts with an upward velocity of 64 feet per second.
* Initial Position: The rocket starts at ground level, so its initial height is 0 feet.
The Formula
The general form of a quadratic function is:
* h(t) = at² + bt + c
Where:
* h(t) is the height of the rocket at time 't'
* a is half the acceleration due to gravity ( -16 in our case)
* b is the initial velocity (64 in our case)
* c is the initial height (0 in our case)
Putting it Together
Substituting the values we get:
h(t) = -16t² + 64t + 0
Simplifying, the quadratic function representing the rocket's height is:
h(t) = -16t² + 64t
