Respuesta :
Answer:
the cannon ball's maximum height is 21 meters rounded to the nearest whole number
Step-by-step explanation:
The maximum height of the cannonball will be 21.06 meters when the time t = 0.9375 seconds.
What is the parabola?
It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
A cannonball has been catapulted through the air and follows the path created by the function given below.
f(t) = -16t² + 30t + 7
where f(t) is the height of the cannonball in meters at any given time (t) in seconds.
Then the height of the cannonball will be given by the differentiation. Then we have
[tex]\rm \dfrac{d}{dx} f(t) = -16t^2 + 30 t + 7 \\\\\\\dfrac{d}{dx} f(t) = -32t + 30[/tex]
Then again differentiate to check whether the value is maximum or minimum.
[tex]\rm \dfrac{d^2}{dx^2} f(t) = -32t + 30\\\\\\\dfrac{d^2}{dx^2} f(t) = -32\\\\\\\dfrac{d^2}{dx^2} f(t) < 0[/tex]
Then the value of the height will be maximum for f'(t) = 0.
f'(t) = 0
-32t + 30 = 0
t = 30/32
t = 0.9375
Then the maximum height will be
f(t) = -16(0.9375)² + 30(0.9375) + 7
f(t) = -14.0625 + 28.125 + 7
f(t) = 21.0625
f(t) = 21.06 meters
More about the parabola link is given below.
https://brainly.com/question/8495504
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