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BigorU [14]
3 years ago
12

The height h of a projectile is a function of the time t it is in the air. the height in feet for t seconds is given by the func

tion h(t) = −16t2 + 96t. what is the domain of the function? what does the domain mean in the context of the problem?
Mathematics
2 answers:
alexgriva [62]3 years ago
7 0

Domain means the values of independent variable(input) which will give defined output to the function.

Given:

The height h of a projectile is a function of the time t it is in the air. The height in feet for t seconds is given by the function

h(t)=-16t^2 + 96t

Solution:

To get defined output, the height h(t) need to be greater than or equal to zero. We need to set up an inequality and solve it to find the domain values.

To \; find \; domain:\\\\h(t) \geq0\\\\-16t^2+96t \geq  0\\Factoring \; -16t \; in \; the \; left \; side \; of \; the \; inequality\\\\-16t(t-6) \geq  0\\Step \; 1: Find \; Boundary \; Points \; by \; setting \; up \; above \; inequality \; to \; zero.\\\\t(t-6)=0\\Use \; zero \; factor \; property \; to \; solve\\\\t=0 \; (or) \; t = 6\\\\Step \; 2: \; List \; the \; possible  \; solution \; interval \; using \; boundary \; points\\(- \infty,0], \; [0, 6], \& [6, \infty)

Step \; 3:Pick \; test \; point \; from \; each \; interval \; to \; check \; whether \\\; makes \; the \; inequality \; TRUE \; or \; FALSE\\\\When \; t = -1\\-16(-1)(-1-6) \geq  0\\-112 \geq  0 \; FALSE\\(-\infty, 0] \; is \; not \; solution\\Also \; Logically \; time \; t \; cannot \; be \; negative\\\\When \; t = 1\\-16(1)(1-6) \geq  0\\80 \geq  0 \; TRUE\\ \; [0, 6] \; is \; a \; solution\\\\When \; t = 7\\-16(7)(7-6) \geq  0\\-112 \geq  0 \; FALSE\\ \; [6, -\infty) \; is \; not \; solution

Conclusion:

The domain of the function is the time in between 0 to 6 seconds

0 \leq  t \leq  6

The height will be positive in the above interval.

Pepsi [2]3 years ago
3 0

Answer:

The answer is explained below

Step-by-step explanation:

STEP 1

A projectile motion is the motion is a specific particle in a curve path, under the influence of gravity.

Domain denotes to a set of values of input for which there is a specific output.

STEP 2

The equation used for projectile motion is:

                    <em>h(t)= - 16t^2 + 96t</em>

It is a kind of function in which time (t) is the input and height (h) is the output.  Here the domain for the function refers to all possible value of time t for which there is an output h (t). IN simple words, domain is the set of all the values of time t for which the particle is in a projectile motion.

STEP 3

The particle begins the motion from ground, goes in projectile and then returns to ground again. Since at ground level, h (t) = 0

So, using the projectile equation:

<em>h(t)= - 16t^2 + 96t</em>

<em>-16t(t-6)= 0</em>

<em>SO, t = 0,6</em>

<em>It will take 6 seconds for the particle to reach the ground again. </em>

<em>The domain of the projectile motion is the set of all set of all the values from 0 to 6 which is {0,6}</em>

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