a catapult launches a boulder with an upward velocity of 122 feet per second. the height of the boulder, (h), in feet after t seconds is given by the function h(t)=-16t^2+122t+10. how long does it take the boulder to reach its maximum height? round to the nearest hundreth, if necessary.
reaches a maximum heught of 15.42 feet after 7.71 seconds
reaches a maximum height of 7.71 feet after 3.81 seconds
reaches a maximum height of 242.56 feet after 7.62 seconds
reaches a maximum height of 242.56 feet after 3.81 seconds
The function h(t) = -16t^2 + 122t + 10 represents the height of the boulder at time t.
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 formula for the x-coordinate of the vertex of a quadratic function in the form f(x) = ax^2 + bx + c is x = -b / (2a).
In this case, a = -16 and b = 122. Plugging these values into the formula, we get:
t = -122 / (2*(-16))
t = -122 / (-32)
t = 3.81
Therefore, the boulder takes approximately 3.81 seconds to reach its maximum height.