. A catapult launches a boulder with an upwark velocity pf 184 feet per second. the heigh of the boulder in feet after t seconds is given by the function h(t)=-16t^2+184t+20. how long does it take the boulder to reach its maximum height? What is the boulders maximum height? Round to the nearest hundredth.
Reaches a maximum height of 11.6 feet after 5.75
Reaches a maximum height of 549 feet after 11.5 seconds
Reaches a maximum height of 549 feet after 5.75 seconds
Reaches a maximum height of 23.2 feet after 11.6 seconds. <---- My answer
Does anyone know if i'm correct?
the x of the vertex is -b/(2a) = -184/(-32)
= 5.75 seconds
plug that into the function
h(5.75) = 16(5.75^2) + 184(5.75) + 20
= 549 ft
Mrs sue or Damon am I correct?
To find the time it takes for the boulder to reach its maximum height, you need to determine the vertex point of the quadratic function representing the height of the boulder. The vertex point (t, h) can be found using the formula t = -b / (2a), where a, b, and c are coefficients in the quadratic function.
In this case, the quadratic function is h(t) = -16t^2 + 184t + 20, so a = -16 and b = 184.
Using the formula t = -b / (2a), we can calculate:
t = -184 / (2(-16))
t = -184 / (-32)
t = 5.75
Therefore, the boulder reaches its maximum height after 5.75 seconds.
To find the maximum height, substitute the value you found for t back into the function.
h(5.75) = -16(5.75)^2 + 184(5.75) + 20
Using this calculation, you should find that the boulder's maximum height is approximately 549 feet.
That means the correct answer is "Reaches a maximum height of 549 feet after 5.75 seconds."