Answer:
f(t) = 15.06 m
Step-by-step explanation:
The relationship between the height of the rocket and the time after launch, t. In seconds is given by :
[tex]f(t) = - 4.9t ^ 2 + 16t + 2[/tex]
We need to find the maximum height the rocket will reach the ground.
When it reaches the ground,
f(t) = 0
So,
Maximum height,
f'(t) = 0
[tex]-9.8t+16=0\\\\t=\dfrac{16}{9.8}\\\\t=1.63\ s[/tex]
Put t = 1.63 in equation (1).
[tex]f(1.63) = - 4.9\times (1.63 ^ 2) + 16(1.63) + 2\\\\=15.06\ m[/tex]
So, the maximum height of the rocket is 15.06 m.
