Arocket is launched from the top of a 101-foot cliff with an initial velocity of 116 ft/s. a. substitute the values into the vertical motion formula h = –16t2 + vt + c. let h = 0. b. use the quadratic formula to find out how long the rocket will take to hit the ground after it is launched. round to the nearest tenth of a second.

It take the rocket 8 seconds to hit the ground after it is launched.

Let h represent the height of the rocket at time t.

The height (h) is given by:

h = –16t² + vt + c

Since the initial velocity (v) = 116 ft/s, the initial height c = 101 ft, hence:

h = –16t² + 116t + 101

Hence, the rocket touches the ground at time h = 0, hence:

0 = -16t² + 116t + 101

Hence, t = 8 seconds.

Therefore it take the rocket 8 seconds to hit the ground after it is launched.

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