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son4ous [18]
3 years ago
14

A rocket is launched from the top of a 99-foot cliff with an initial velocity of 122 ft/s.

Mathematics
2 answers:
Mazyrski [523]3 years ago
8 0

0 = –16t2 + 122t + 99; 8.4 s

should be the right answer!!

Harman [31]3 years ago
5 0
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:
0=-16 t^{2} +122t+99
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:
-99=-16 t^{2} +122t+99
-16 t^{2} +122+198=0

Now we can apply the quadratic formula t= \frac{-b+or- \sqrt{ b^{2} -4ac} }{2a} where a=-16, b=122, and c=198
t= \frac{-122+or- \sqrt{ 122^{2}-(4)(-16)(198) } }{(2)(-16)}
t= \frac{-122+ \sqrt{27556} }{-32} or t= \frac{-122- \sqrt{27556} }{-32}
t= \frac{-122+166}{-32} or t= \frac{-122-166}{-32}
t= \frac{-11}{8} or t=9

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