To find the time it takes to reach the maximum height, we need to first find the vertex of the parabolic function h(t) = -5t^2 + 92t + 16.
The formula for the t-coordinate of the vertex of a parabola in the form y = ax^2 + bx + c is given by t = -b/2a.
In this case, a = -5 and b = 92.
Therefore, t = -92 / (2(-5)) = -92 / (-10) = 9.2 seconds.
To find the maximum height, we substitute t = 9.2 seconds into the equation h(t):
h(9.2) = -5(9.2)^2 + 92(9.2) + 16
h(9.2) = -5(84.64) + 844.4 + 16
h(9.2) = -423.2 + 844.4 + 16
h(9.2) = 437.2
Therefore, it takes 9.2 seconds for the boulder to reach its maximum height, which is 437.2 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 = -5?+ 92 + 16. How
long does it take to reach maximum height? What is the boulder's maximum height?
Round to the nearest hundredth, if necessary.
1 answer
1 answer