Question
A model rocket is fired into the air. Its height above the ground is given by the equation
y = -16x2 + 344x
where x represents the time (in seconds) since the rocket was launched, and y represents the rocket's height (in feet) above the ground.
Round all answers below to two decimal places, if necessary.
What is the maximum height above the ground that the rocket reaches? feet
After how much time does the rocket reach this height? seconds
y = -16x2 + 344x
where x represents the time (in seconds) since the rocket was launched, and y represents the rocket's height (in feet) above the ground.
Round all answers below to two decimal places, if necessary.
What is the maximum height above the ground that the rocket reaches? feet
After how much time does the rocket reach this height? seconds
Answers
GPT 3.5
To find the maximum height that the rocket reaches, we first need to determine the vertex of the parabolic equation y = -16x^2 + 344x.
The x-coordinate of the vertex of a parabola given by the equation y = ax^2 + bx + c is given by x = -b/(2a). In this case, a = -16 and b = 344.
x = -344/(2*(-16)) = -344/-32 = 10.75 seconds
Now, substitute x = 10.75 seconds back into the original equation to find the maximum height of the rocket:
y = -16(10.75)^2 + 344(10.75)
y = -16(115.56) + 3694
y = -1849.74 + 3694
y = 1844.26 feet
Therefore, the maximum height above the ground that the rocket reaches is 1844.26 feet.
The rocket reaches this maximum height after 10.75 seconds.
The x-coordinate of the vertex of a parabola given by the equation y = ax^2 + bx + c is given by x = -b/(2a). In this case, a = -16 and b = 344.
x = -344/(2*(-16)) = -344/-32 = 10.75 seconds
Now, substitute x = 10.75 seconds back into the original equation to find the maximum height of the rocket:
y = -16(10.75)^2 + 344(10.75)
y = -16(115.56) + 3694
y = -1849.74 + 3694
y = 1844.26 feet
Therefore, the maximum height above the ground that the rocket reaches is 1844.26 feet.
The rocket reaches this maximum height after 10.75 seconds.