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Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. A rocket is launched from atop a 101-foot cliff with an initial velocity of 116 ft/s. a. Substitute the values into the vertical motion formula h= -16t^2 +vt +c . Let h = 0. b. Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.

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altavistard
Here the vertical motion formula is   h = -16t^2 + 116t + 101 (feet)

How long will it take for the rocket to rise, stop rising, start falling and then his the ground?  To find this, set h = 0 and solve for t.  Omit negative results, if any.

-16t^2 + 116t + 101 = 0.

Since the solutions are unlikely to be "nice" numbers (integers), let's use the quadratic formula to solve this equation for t:

        -116 plus or minus sqrt(116^2 - 4(-16)(101) )
t  = ----------------------------------------------------------------
                              2(-16)
        -116 plus or minus sqrt(19920)
   = ---------------------------------------------
                           -32
        -116 plus or minus 141.1
    = -----------------------------------
                          -32

   = -25.1/(-32) (discard)            and           t = -116 - 141.1
                                                                        ------------------
                                                                               -32
                         
                                                                    t = 8.03.

The rocket will hit the ground 8.03 seconds after it is launched.

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