a boulder is thrown launched into the air with an upward velocity of 184 ft per second. Its height h in feet after t seconds is given by the function h(t)=-16t^2 +184t+6. How long does it take the boulder to reach its maximum height? What is the boulder maximum height?
a. V = Vo + g*t.
0 = 184 - 32*t
t = ?
b. Use the given Eq. and the calculated value of t to find max. ht.
To find the time it takes for the boulder to reach its maximum height, we need to determine the vertex of the quadratic function. The vertex of a quadratic function in the form of h(t) = at^2 + bt + c can be found using the formula t = -b / (2a).
In this case, the function representing the height of the boulder is h(t) = -16t^2 + 184t + 6.
Comparing this to the general form of a quadratic function, we have a = -16, b = 184, and c = 6.
Using the formula, t = -b / (2a), we can substitute the values to find the time it takes for the boulder to reach its maximum height:
t = -184 / (2 * -16)
t = -184 / -32
t = 5.75 seconds
Therefore, it takes the boulder 5.75 seconds to reach its maximum height.
To find the maximum height, we can substitute the value of t we just found (5.75 seconds) into the height function h(t):
h(5.75) = -16(5.75)^2 + 184(5.75) + 6
Calculating this expression will give us the maximum height of the boulder.