Question

A jet fighter pilot wishes to accelerate from rest at 5 ggg to reach Mach-3 (three times the speed of sound) as quickly as possible. Experimental tests reveal that he will black out if this acceleration lasts for more than 5.2 ss . Use 331 m/sm/s for the speed of sound

Answer 1

Answer

given,

acceleration, a = 5 g =  5 x 9.8 = 49 m/s²

speed of sound, v = 331 m/s

speed , v = 3 Mach = 3 x 331 m/s = 993 m/s

time, t = 5.2 s

a) Calculating the time period of black out.

  time required by the aircraft to black out

 using equation of motion

  v = u + a t

 initial velocity = 0 m/s

  993 = 0 + 49 t

   t = 20.26 s

the required time to reach 3 Mach speed is more than the given time hence, pilot will black out.

b) now, calculating the maximum speed it can reach in 5.2 s

 using equation of motion

  v = u + a t

 initial velocity = 0 m/s

  v = 0 + 49 x 5.2

 v = 254.8 m/s