Assume D=2ow2 gives the drag force on a pilot plus ejection seat just after they

Question

Assume D=2ow2 gives the drag force on a pilot plus ejection seat just after they are ejected from a plane traveling horizontally at 1500 km/h. Assume also that the mass of the seat is equal to the mass of the pilot and that the drag coefficient is that of a sky diver. Assume the pilot's mass is 72 kg and using ve = 60 m/s for a single sky diver estimate the magnitudes of a the drag force on the pilot + seat and b) the ratio of the horizontal deceleration to g, both just after ejection. (The result ot (a) should indicate an engineering requirement: The seat must include a protective barrier to detlect the initial wind blast away from the pilot's head.) (a) Number Units (b) Number Units

Explanation / Answer

the given equation

D = 1/2 * C rho A v^2

formula for terinal velocity is

vt = sqrt 2 F/ C rho A

C rho A = 2 mg/ vt

D = 1/2 * ( 2 mg/ vt^2) v^2 = mg ( v/ vt)^2

= 72 * 9.8 ( 1500 ( 1000/ 3600)/ 60)^2

=34027.777 N

(b)

We assume the mass of the ejection seat is roughly equal to the mass of the pilot.
Thus, Newton’s second law (in the horizontal direction) applied to this system of mass

a= D/ 2m= g/2 ( v/ vt)^2 = g/2 ( 1500 ( 1000/ 3600)/ 60)^2= 24.11

a/g = 24.11

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