A catapult launches of Boulder with an upward velocity of 122 ft per second the height of the boulder h in the feet after 2 seconds given by the function of H t equals 16t squared plus 122t + 10 how long does it take for the boulder to reach the maximum weight what is the bowler's maximum weight round to the nearest hundredth if necessary
To find the time it takes for the boulder to reach its maximum height, we need to determine the vertex of the function h(t) = -16t^2 + 122t + 10.
The vertex of a quadratic function in the form y = ax^2 + bx + c is given by the formula (-b/2a, f(-b/2a)), where f(x) is the function.
In this case, a = -16 and b = 122.
So, the time it takes for the boulder to reach the maximum height is given by t = -122 / 2(-16) = 3.8125 seconds.
Substitute t = 3.8125 into the function h(t) to find the maximum height reached by the boulder:
h(3.8125) = -16(3.8125)^2 + 122(3.8125) + 10
h(3.8125) = -234.375 + 464.75 + 10
h(3.8125) = 240.375 feet
Therefore, the time it takes for the boulder to reach the maximum height is approximately 3.81 seconds, and the maximum height reached by the boulder is approximately 240.38 feet.