Answer:
t = .51 sec and t = 12.24 sec
Step-by-step explanation:
This is parabolic. The nature of the parabola is symmetrical about a vertical line, so when an object going up passes a certain height, it will reach its max height and begin to fall, once again passing that certain height, just at a later time. Besides that, this is a second degree polynomial so we are expecting to have 2 solutions.
If we are looking for the times that the height, h, of the rocket is 100 feet, then we sub in 100 for h and factor to solve for t:
[tex]100=-16t^2+204t[/tex]
To factor this, we will move everything over to one side and set the quadratic equal to 0:
[tex]-16t^2+204t-100=0[/tex]
Factor this using the quadratic formula to find
t = .51 and t = 12.24 seconds
