Answer:
1) h(t) = -16t² + 300t + 50
2) h'(t) = -32t + 300
-32t + 300 = 0
t = 9.375 sec.
3) h(9.375) = 1,456.25 ft.
4) 16t² - 300t - 50 = 0
8t² - 150t - 25 = 0
(-150)² - 4(8)(-25) = 23,300
t = (150 ± √23,300)/16
= (150 + 10√233)/16
= (75 + 5√233)/8
= about 18.92 sec.
5) -16t² + 300t + 50 = 1,200
-16t² + 300t - 1,150 = 0
16t² - 300t + 1,150 = 0
8t² - 150t + 525 = 0
(-150)² - 4(8)(525) = 5,700
t = (150 ± √5,700)/16
= (150 ± 10√57)/16
= (75 ± 5√57)/8
4.66 sec. < t < 14.09 sec.
