Assume that John Travoltage and the carpet are neutral to start. After he rubbed his foot on the carpet on took negatives, what charge is on the carpet and why

Same charge, positive.

Please see below as the answer is self-explanatory.

Explanation:

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