Abullet of mass m = 40~\text{g}m=40 g, moving horizontally with speed vv, strikes a clay block of mass m = 1.53m=1.53 kg that is hanging on a light inextensible string of length l = 0.587l=0.587. the bullet becomes embedded in the block, which was originally at rest. what is the smallest value of vv which would cause the block-on-a-string to swing around and execute a complete vertical circle?

An object with initial temperature 130 ∘ f is submerged in large tank of water whose temperature is 50 ∘ f . find a formula for f ( t ) , the temperature of the object after t minutes, if the cooling constant is k = − 0.2 . remember newton's law of cooling (the rate of change of temperature with respect to time is equal to k times the difference between the temperature of the object and the surrounding temperature) ! : )