Arocket is launched from the top of a 99-foot cliff with an initial velocity of 122 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. the work for the solutions would be great

Remember that c is the initial height. Since we the rocket is in a 99-foot cliff, c=99. Also, we know that the velocity of the rocket is 122 ft/s; therefore v=122
Lets replace the values into the the vertical motion formula to get:

Notice that the rocket hits the ground at the bottom of the cliff, which means that the final height is 99-foot bellow its original position; therefore, our final height will be h=-99
Lets replace this into our equation to get:



Now we can apply the quadratic formula  where a=-16, b=122, and c=198

or 
or 
or 

Since the time can't be negative, we can conclude that the rocket hits the ground after 9 seconds.

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