To find the time it takes to reach the maximum height, we need to find the vertex of the parabolic function h = -5t^2 + 92t + 16. The formula for the x-coordinate of the vertex is given by x = -b/2a, where the equation is in the form y = ax^2 + bx + c.
In this case, a = -5 and b = 92. Plugging these values into the formula, we get:
t = -92 / 2*(-5) = -92 / -10 = 9.2 seconds
Therefore, it takes 9.2 seconds for the boulder to reach the maximum height.
To find the maximum height, we substitute t = 9.2 seconds into the equation h = -5t^2 + 92t + 16:
h = -5(9.2)^2 + 92(9.2) + 16
h ≈ 424.8 meters
Therefore, the boulder's maximum height is approximately 424.8 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. How long does it take to reach maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary.
3 answers
see if the maximum height is 439 meters
Let's re-calculate the maximum height using t = 9.2 seconds:
h = -5(9.2)^2 + 92(9.2) + 16
h = -5(84.64) + 846.4 + 16
h = -423.2 + 846.4 + 16
h = 439.2 meters
Therefore, the maximum height of the boulder is approximately 439.2 meters. This confirms that the maximum height is 439 meters.
h = -5(9.2)^2 + 92(9.2) + 16
h = -5(84.64) + 846.4 + 16
h = -423.2 + 846.4 + 16
h = 439.2 meters
Therefore, the maximum height of the boulder is approximately 439.2 meters. This confirms that the maximum height is 439 meters.