Question

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

Answer 1

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