\"An airplane A is performing a loop with constant radius p = 254 m....\" An air

Question

"An airplane A is performing a loop with constant radius p = 254 m...."

An airplane A is performing a loop with constant radius p = 254 m. From elementary physics, we know that the acceleration of a point in uniform circular motion (i.e.. circular motion at constant speed) is directed toward the center of the circle and has magnitude v* equal to -. where v is the speed. Assuming that A can maintain its speed constant and P using the component system shown, provide the expressions of the velocity and acceleration of A when 6 = 30degree and | a | = 2g. where a is the acceleration of A and g is the acceleration due to gravity.

Explanation / Answer

we know that v^2/p = a = 2g ...(net force = centtripetal force in constant speed circular motion)

Given its at 30 degrees ..Speed = sqrt(2*g*p) = sqrt(2*9.81*254) = 70.6 m/s

Direction of accelerationis along the radius at angle 30 degrees to y axis..

so a = -2*g * sin(30 deg) i + 2*g*cos(30 deg) j = -9.81 i + 17 j

Velocity = 70.6cos(30 deg) i + 70.6sin(30 deg) j = 61.14 i + 35.3 j

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