If triply the force is exerted over triple the distance, how does the resulting increase in kinetic energy compare with the original increase in kinetic energy?

Kinetic energy will be 9 times of initial energy

Explanation:

Let the initial force is F and initially the distance is d

So work done by the force

From energy theorem we know that

Work done is equal to kinetic energy

So

Now force is tripled so new force = 3F

And distance is also tripled so new distance

New kinetic energy

So kinetic energy will be 9 times of initial energy

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