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Chapter 1: Q25E (page 94)

A jet plane comes in for a downward dive as shown in Fig. E3.25. The bottom part of the path is a quarter circle with a radius of curvature of 280 m. According to medical tests, pilots will lose consciousness when they pull out of a dive at an upward acceleration greater than 5.5g. At what speed (in m/s and in mph) will the pilot black out during this dive?

Short Answer

Expert verified

The velocity of pilot during the dive is 128.8 m/s or 274.7 mph.

Step by step solution

01

Identification of given data:

The given data can be listed below,

  • The radius of curvature of the path is, R = 280 m
  • The radial acceleration of the pilots is, ar=5.5g=5.5脳9.8m/s2=53.9m/s2.
02

Concept/Significance of radial velocity:

A particle's velocity along the observer's line of sight is known as its radial component. It is a part of a radial direction change in location per unit of time.

03

Determination of the speed (in m/s and in mph) will the pilot blackout during the dive:

The velocity of the pilot is given by,

ar=v2Rv=arR

Here, ar is the radial acceleration, and R is the radius of the path.

Substitute all the values in the above expression.

v=53.9m/s2280m=122.8m/s1mph0.4770m/s=274.7mph

Hence, the velocity of pilot during the dive is 128.8 m/s or 274.7 mph.

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