A firecracker is launched straight up, and its height is a function of time, h(t)= -14^2 + 112t, where h is the height in feet and t is the time in seconds with t=0 corresponding to the instant it launches. What is the height 5 seconds after launch? What is the domain of this function?
To find the height 5 seconds after launch, we need to substitute t = 5 into the given function h(t) = -14^2 + 112t and solve for h.
So, let's calculate the height:
h(5) = -14(5)^2 + 112(5)
First, we square 5:
h(5) = -14(25) + 112(5)
Next, we simplify:
h(5) = -350 + 560
h(5) = 210
Therefore, the height 5 seconds after launch is 210 feet.
Now, let's determine the domain of this function. The domain of a function is the set of all possible input values (in this case, time values) for which the function is defined.
In this case, the function is defined for all real numbers for t, as there are no constraints or restrictions given.
Therefore, the domain of this function is all real numbers, or (-infinity, +infinity).