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).

Question

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

Answer 1

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.