Question

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 = –5t2+ 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. (1 point)

Reaches a maximum height of 16.00 meters in 18.4 seconds.
Reaches a maximum height of 18.57 meters in 9.2 seconds.
Reaches a maximum height of 37.14 meters in 18.4 seconds.
Reaches a maximum height of 439.20 meters in 9.2 seconds.

Answer 1

[AI-generated answer — Bot GPT 3.5]

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 time to reach the maximum height is given by t = -b/2a, where in this case a = -5 and b = 92.

Plugging in the values:
t = -92 / 2(-5)
t = -92 / -10
t = 9.2 seconds

So, it takes 9.2 seconds to reach the maximum height.

To find the maximum height, we plug t = 9.2 into the equation h = –5t^2 + 92t + 16.
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 boulder's maximum height is 439.20 meters.