A350-g air track cart on a horizontal air track is attached to a string that goes over a frictionless pulley with a moment of inertia of 6.00 × 10-6 kg ∙ m2 and a radius of 1.35 cm. if the string is pulled vertically downward by a force of 2.50 n,
(a) what is the magnitude of the acceleration of the cart?
(b) what is the tension in the horizontal string between the pulley and the cart?

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initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft