Final answer:
The domain of the function that represents a jump on a trampoline is from t = 0 to t = 1.5, inclusive. This is because the time of the jump starts when you leave the trampoline (t = 0) and ends when you land back on it (t = 1.5)
Step-by-step explanation:
The domain of a function refers to all possible input values, or in this context, the time in seconds during which you are jumping, denoted by t. So, for a person jumping on a trampoline, time cannot be negative; you cannot jump before you start jumping. Time starts when you leave the trampoline (t = 0) and ends when you return back to the trampoline.
To find when you return back to the trampoline, we set y, the height above the trampoline, to 0 and solve for t in the equation y = -16t2 + 24t. This equation is a quadratic and hence can be solved either by factoring or using the quadratic formula t = [-b ± sqrt(b2 -4ac)] / (2a).
On solving, we get two solutions, t = 0 and t = 1.5. The physical interpretation of these solutions is that at t = 0, you start your upwards motion and at t = 1.5 you land back on the trampoline. Therefore, the domain of the function in this problem is from t = 0 to t = 1.5, inclusive.
Learn more about Domain of a Function