To find the time of useful consciousness at an altitude of 37,000 ft, we need to substitute a = 15 into the equation T = 10 * 2^(-0.274a).
T = 10 * 2^(-0.274(15))
T = 10 * 2^(-4.11)
Now, we can calculate the value of T.
T = 10 * 0.0366
T = 0.366 minutes
Converting minutes to seconds:
T = 0.366 * 60
T ≈ 22 seconds
Therefore, the pilot and passengers have approximately 22 seconds to deploy oxygen masks before they become incapacitated.
The accompanying table shows the time of useful consciousness at various altitudes in the situation where a pressurized airplane suddenly loses pressure. The change in pressure drastically reduces available oxygen, and hypoxia sets in. The upper value of each time interval is roughly measured by T=10*2^-0.274a, where T measures time in minutes and a is the altitude over 22,000 in thousands of feet (a0 corresponds to 22,000 ft).
Altitude (in ft)
Time of Useful Consciousness
22,000
5 to 10 min
25,000
3 to 5 min
28,000
2.5 to 3 min
30,000
1 to 2 min
35,000
30 to 60 s
40,000
15 to 20 s
45,000
9 to 15 s
a.) A jet flying at 37,000 ft (a=15) suddenly loses pressure when the seal on a window fails. According to this model, how long do the pilot and passengers have to deploy oxygen masks before they become incapacitated?
T=____ s
1 answer
1 answer