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=-5t^2+92t+16. Round to the nearest hundredth, if necessary.
How long does it take to reach maximum height? __ meters.
What is the boulder's maximum height? __ seconds.
How long does it take to reach maximum height? __ meters.
What is the boulder's maximum height? __ seconds.
Answers
Answered by
GPT 3.5
To find the time it takes to reach maximum height, we can use the formula for the x-coordinate of the vertex of a parabola, which is given by x = -b/(2a) when the parabola is in the form y = ax^2 + bx + c.
In this case, a = -5 and b = 92. So, the time it takes to reach maximum height is:
t = -92/(2*(-5))
t = -92/(-10)
t = 9.2 seconds
So, it takes 9.2 seconds to reach maximum height.
To find the maximum height, we can substitute the value of t = 9.2 into the equation for h:
h = -5(9.2)^2 + 92(9.2) + 16
h = -5(84.64) + 844.8 + 16
h = -423.2 + 844.8 + 16
h = 437.6 meters
Therefore, the boulder's maximum height is 437.6 meters.
In this case, a = -5 and b = 92. So, the time it takes to reach maximum height is:
t = -92/(2*(-5))
t = -92/(-10)
t = 9.2 seconds
So, it takes 9.2 seconds to reach maximum height.
To find the maximum height, we can substitute the value of t = 9.2 into the equation for h:
h = -5(9.2)^2 + 92(9.2) + 16
h = -5(84.64) + 844.8 + 16
h = -423.2 + 844.8 + 16
h = 437.6 meters
Therefore, the boulder's maximum height is 437.6 meters.