To find the time it takes for the boulder to reach its maximum height, we need to find the vertex of the parabolic function. The x-coordinate of the vertex is given by the formula -b/2a, where a, b, and c are the coefficients in the quadratic equation ax^2 + bx + c = 0.
In this case, a = -16 and b = 184, so the time it takes for the boulder to reach its maximum height is:
t = -b/2a = -(184)/(2(-16)) = 5.75 seconds
To find the maximum height, we need to plug this value of t into the equation for h(t) and simplify:
h(5.75) = -16(5.75)^2 + 184(5.75) + 20 = 549
Therefore, the boulder reaches a maximum height of 549 feet after 5.75 seconds. The answer is choice C.
A catapult launches a boulder with an upward velocity of 184 feet per second. The height of the boulder, (h), in feet after t seconds is given by the function h of t equals negative 16t squared plus 184t plus 20 . How long does it take the boulder to reach its maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary.
A. Reaches a maximum height of 11.6 feet after 5.75 seconds.
B. Reaches a maximum height of 549 feet after 11.5 seconds.
C. Reaches a maximum height of 549 feet after 5.75 seconds.
D. Reaches a maximum height of 23.2 feet after 11.6 seconds.
1 answer
1 answer