To find the time it takes to reach maximum height, we need to determine the vertex of the function h(t) = -5t^2 + 92t + 16. The formula for the x-coordinate of the vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by x = -b/(2a).
In this case, a = -5 and b = 92. Plugging these values into the formula, we get:
t = -92 / (2*(-5))
t = -92 / (-10)
t = 9.2 seconds
So, the boulder takes 9.2 seconds to reach its maximum height.
To find the maximum height, we substitute t = 9.2 back into the function h(t) = -5t^2 + 92t + 16:
h(9.2) = -5(9.2)^2 + 92(9.2) + 16
h(9.2) = -5(84.64) + 844.8 + 16
h(9.2) = -423.2 + 844.8 + 16
h(9.2) = 437.6
Therefore, the boulder's maximum height is approximately 437.6 meters.
A catapult launches a boulder with an upward velocity of 92 m/s. The height of the boulder, h, in meters after t seconds is given by the function h=−5t^2+92t+16
. Round to the nearest hundredth, if necessary.(2 points)
How long does it take to reach maximum height? __ meters
What is the boulder's maximum height? __ seconds
1 answer