What is the magnitude of the maximum velocity that a 0.3–kilogram mass attached to a 0.75–meter string can have if the mass is whirled around in a circular horizontal path? The maximum tension that the string can withstand is 250 newtons.

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