## The Best Answer for How far to the right of where the string was cut does the ball hit the floor?

Let:

T be the tension in the string,

m be the mass of the ball,

g be the acceleration due to gravity,

u be the horizontal speed of the ball when the string is cut,

r be the radius of the circle,

x be the horizontal distance to where the ball lands,

t be the time between cutting and landing,

h be the height of the ball above the floor when the string is cut.

T - mg = mu^2 / r ...(1)

x = ut ...(2)

h = gt^2 / 2 ...(3)

Eliminating t from (2) and (3):

x^2 = 2hu^2 / g

From (1):

u^2 = r(T / m - g)

Eliminating u^2:

x^2 = 2hr(T / m - g) / g

= 2hr(T / [ mg ] - 1)

x = sqrt{ 2 * (2.00 - 0.60)0.60(4.4 / [0.110 * 9.81] - 1) }

= 2.27 m.

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