The results of the quadratic equation are, respectively:
Question 1: Initial height of the stomp rocket.
Question 2: Related to the velocity of the stomp rocket.
Question 3: Related to gravitational acceleration of the stomp rocket.
Question 4: The stomp rocket shall hit the ground approximately 6.25 seconds.
How to analyze quadratic equation
The figure attached below shows the height of the stomp rocket (h), in feet, as a function of time (t), in seconds. The quadratic equation represents the free-fall of the stomp rocket, that is, that rocket is accelerated uniformly due to gravity. The model is introduced below:
h(t) = h' + v · t - 0.5 · g · t²
Where:
- h' - Initial height, in feet.
- v - Initial velocity, in feet per second.
- g - Gravitational acceleration, in feet per square second.
Now we proceed to answer each question:
Question 1: The constant 5 represents the initial height of the stomp rocket.
Question 2: The component 100 · t is related to the velocity of the stomp rocket.
Question 3: The component - 16 · t² is related to gravitational acceleration of the stomp rocket.
Question 4: The stomp rocket shall hit the ground approximately 6.25 seconds.