Question

When a cannon balls fired the equation of his pathway can be modeled by h= -16t^2 + 128t
find the maximum height of the cannonball and find a time it will take for the cannonball to reach the ground

Answer 1

Answer:

The maximum height of the cannonball  'h' = 256

The time will take for the cannonball to reach the ground 't' =4

Step-by-step explanation:

Explanation:-

The given equation  h(t) = -16 t² + 128 t   ...(i)

Differentiating equation(i) with respective to 't' we get

$h^{l} (t) = \frac{dh}{dt} = -16 (2 t) +128 (1)$

$h^{l} (t) = -16 (2 t) +128 (1) = 0$

$-32 t +128 = 0$

- 32 t = -128

    t = 4

Now

Again differentiating with respective to 'x'

$h^{ll} (t) = \frac{d^{2} h}{dt^{2} } = -16 (2 ) < 0$

The function is Maximum at  t = 4

The maximum value

h(t) =-16 t² + 128 t  

h(4) = - 16 (4)² + 128(4) = 256

Conclusion:-

The maximum height of the cannonball  'h' = 256

The time will take for the cannonball to reach the ground 't' =4