To find the boulder's maximum height, we need to find the vertex of the parabolic function h = -16t^2 + 120t + 10. The formula for the x-coordinate of the vertex of a parabola in the form y = ax^2 + bx + c is given by x = -b/2a. In this case, a = -16 and b = 120, so we have:
x = -b/2a = -120/(2*(-16)) = 3.75
Therefore, the boulder reaches its maximum height after 3.75 seconds.
To find the maximum height, we substitute t = 3.75 into the equation for h:
h = -16(3.75)^2 + 120(3.75) + 10 ≈ 168.75
Therefore, the boulder's maximum height is approximately 168.75 feet.
A catapult launches a boulder with an upward velocity of 120 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h = –16t2 + 120t + 10. How long does it take to reach maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary.
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