Answer:
Time required to hit the ground is 7.9 s.
Step-by-step explanation:
The height of the rocket is given by
[tex]y =- 16 x^2 + 119 x + 57[/tex]
For the time to hit the ground, put y = 0
[tex]-16x^2+119x+57=0\\\\16 x^2 - 119 x - 57 = 0 \\\\x = \frac{119\pm\sqrt{14161+3648}}{32}\\\\x = \frac{119\pm133.45}{32}\\\\t = - 0.45 s, 7.9 s[/tex]
Time cannot be negative, so time to hit the ground is 7.9 s.