A toy rocket is launched straight upward from the ground. The height of the rocket above the ground, measured in feet, is given by the equation h(t) = -16t^2 + 64t, where t represents time in seconds. Determine the domain, using interval notation, for this function within the given context.
Mathematics · High School · Thu Feb 04 2021
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In the context of the given problem, the domain refers to all the possible values of time (t) during which the height (h(t)) of the rocket can be measured. Since we are talking about a real-life toy rocket, the domain consists only of the time from when the rocket is launched until it lands back on the ground.
To determine when the rocket lands, we need to find when the height is equal to zero (since it's back on the ground). We set h(t) = 0 and solve for t:
0 = -16t^2 + 64t
Factor out the common factor, which in this case is t:
t(-16t + 64) = 0
This gives us two solutions: t = 0 and t = 4.
t = 0 represents the time of launch and t = 4 represents the time in seconds when the rocket lands back on the ground. No other values for t make sense in this real-world context (e.g., negative time or time after the rocket has already landed). Hence, the domain of the function h(t), in interval notation, is [0, 4].