Question

Partner Practice: A toy rocket is launched from the ground straight upward. The height of the rocket above the ground, in feet, is given by the equation h(t)=-16t^(2)+64t, where t is the time in seconds. Determine the domain for this function in the given context. Explain

Answer 1

The domain of the function h(t) = -16t^(2)+64t, which represents a toy rocket's flight from the ground and back, is [0, 4]. This shows that the rocket was launched at t = 0 sec and returned to the ground at t = 4 sec.

Step-by-step explanation:

The domain of a function encompasses all the possible input values, in this case, the time 't', in the given context. We know that 't', time, must be a non-negative real number since it's not plausible to have negative time. So 't' starts from zero, when the toy rocket is launched.

But how long does it take for the rocket to return to the ground? In the given function h(t) = -16t^(2)+64t, we set h(t) equal to zero and solve for 't' since at ground level, the height h(t) would be zero.

We find that 't' is either 0 or 4. Therefore, the domain of this function within this context is [0, 4], meaning the rocket launched and then returned to the ground after 4 seconds.

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