Question
A catapult launches at Boulder with upward velocity of 92 m/s the height of the boulder H in meters and after 2 seconds is given the function H equals -5t squared plus 92t + 16 how long does it take to reach the maximum height what is the boulders maximum height round to the nearest hundredth if necessary
Answers
GPT 3.5
To find the maximum height of the boulder, we first need to find the time taken to reach the maximum height.
The equation for the height of the boulder is given by:
H(t) = -5t^2 + 92t + 16
To find the time taken to reach the maximum height, we need to find the vertex of the quadratic equation -5t^2 + 92t + 16.
The vertex of a quadratic equation in the form of ax^2 + bx + c is given by t = -b/2a.
In this case, a = -5 and b = 92.
t = -92 / 2(-5)
t = -92 / -10
t = 9.2 seconds
Now, we substitute t = 9.2 seconds back into the equation H(t) to find the maximum height:
H(9.2) = -5(9.2)^2 + 92(9.2) + 16
H(9.2) = -5(84.64) + 846.4 + 16
H(9.2) = -423.2 + 846.4 + 16
H(9.2) = 439.2 meters
Therefore, it takes 9.2 seconds for the boulder to reach the maximum height, and the maximum height reached is 439.2 meters.
The equation for the height of the boulder is given by:
H(t) = -5t^2 + 92t + 16
To find the time taken to reach the maximum height, we need to find the vertex of the quadratic equation -5t^2 + 92t + 16.
The vertex of a quadratic equation in the form of ax^2 + bx + c is given by t = -b/2a.
In this case, a = -5 and b = 92.
t = -92 / 2(-5)
t = -92 / -10
t = 9.2 seconds
Now, we substitute t = 9.2 seconds back into the equation H(t) to find the maximum height:
H(9.2) = -5(9.2)^2 + 92(9.2) + 16
H(9.2) = -5(84.64) + 846.4 + 16
H(9.2) = -423.2 + 846.4 + 16
H(9.2) = 439.2 meters
Therefore, it takes 9.2 seconds for the boulder to reach the maximum height, and the maximum height reached is 439.2 meters.