Superman can leap over tall buildings. WHen he does so, hisheight s (in feet) off the ground after t seconds is given by s = − t 2 + 10 t + 14Foe how many feet is Superman more han 30 feet off the ground?A. 3 secB. 11/2 secC. 13/2 secD. 6 secE. 7 sec

Question

Superman can leap over tall buildings. WHen he does so, hisheight s (in feet) off the ground after t seconds is given by   s  =  −      t          2        +  10  t  +  14Foe how many feet is Superman more han 30 feet off the ground?A. 3 secB. 11/2 secC. 13/2 secD. 6 secE. 7 sec

Clarissa Adkins · Accepted Answer

Solving for t when s = 30:      t          2        −  10  t  +  16  =  0(t-8)(t-2) = 0So s = 30 when t=2 and then again when t=8. This corresponds tosuperman first hitting 30ft on the way up, and then hitting 30 ftagain on the way down. so the total time spent at 30ft or more = 8- 2 = 6 seconds

Lilliana Livingston · Accepted Answer

Superman&#039;s motion is parabolic.   In this case,Superman will be at 30 feet at two times in his jump.Once on his way up and once on his way down.   His timeabove 30 feet is just the difference in these two times. Sofirst we must find when he is at 30 feet. setting s = 30 we have  −      t          2        +  10  t  +  14  =  30  −      t          2        +  10  t  −  16  =  0  −  (      t          2        −  10  t  +  16  )  =  0-(t-8)(t-2)=0He&#039;s on his way up at t=2, and on his way down at t =8.  So he&#039;s above 30 feet for 6 seconds

Superman can leap over tall buildings. WHen he does so, hisheight s (in feet) off the ground after t seconds is given by s=-t^2 +10t+14 Foe how many feet is Superman more han 30 feet off the ground? A. 3 sec B. 11/2 sec C. 13/2 sec D. 6 sec E. 7 sec

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