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What is the magnitude of the acceleration, in \' g \' units (where 1 g = 9.8 m/s

ID: 582347 • Letter: W

Question

What is the magnitude of the acceleration, in 'g' units (where 1 g = 9.8 m/s2), of a pilot whose aircraft enters a horizontal circular turn with a velocity of v0 = (400 x-direction + 500 y-direction) m/sand 24.0 s later leaves the turn with a velocity of vf = (400 x-direction 500 y-direction) m/s. What is the magnitude of the acceleration, in 'g' units (where 1 g = 9.8 m/s2), of a pilot whose aircraft enters a horizontal circular turn with a velocity of v0 = (400 x-direction + 500 y-direction) m/sand 24.0 s later leaves the turn with a velocity of vf = (400 x-direction 500 y-direction) m/s.

Explanation / Answer

We assume the turn is made with uniform circular motion. Then the pilot’s acceleration is centripetal and has
magnitude a given by         a = V^2/R

where R is the circle’s radius

time required to complete a full circle is the period given by T = 2*PI*R/v

Because we do not know radius R, we solve for R

=>R=T*V/(2*PI)

a=V^2/R =V^2/(T*V/(2*PI)) =2*PI*V/(T)

Speed v is the (constant)

magnitude of the velocity during the turning V=sqrt(Vx^2+Vy^2) =sqrt(400^2+500^2) =640.3m/s

As Vf =-Vi => Aircraft completed half revolution in t=24s =>T=48s

=>a =2*PI*640.3/(48) =83.815m^2/s =8.54g m/s^2

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