A small rock falling from the top of a 124-ft-tall building with an initial downward velocity of –30 ft/sec is modeled by the equation h(t) = –16t2 – 30t + 124, where t is the time in seconds. For which interval of time does the rock remain in the air? t = 2 –2 < t < 0 0 < t < 2 t > 2
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Answer:
2 sec
Step-by-step explanation:
h(t) = –16t² – 30t + 124
at t = 0
h(0) = -0 - + 124 = 124 ( height of buliding)
so at t = 0 rock is at top of 124 ft building
let say after t secs it reaches ground so height = 0
–16t² – 30t + 124 = 0
=> 8t² + 15t - 62 = 0
=> 8t² - 16t + 31t - 62 = 0
=> 8t(t -2) + 31(t -2) = 0
=> (8t + 31)(t - 2) = 0
=> t = 2 ( as time can not be -ve)
for 2 sec rock remain in the air before hitting ground
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