You throw a ball of mass 0.4 kg straight up. You observe that it takes 2.1 s to go up and down, returning to your hand. Assuming we can neglect air resistance, the time it takes to go up to the top is half the total time, 1.05 s. Note that at the top the momentum is momentarily zero, as it changes from heading upward to heading downward. (a) Use the momentum principle to determine the speed that the ball had just AFTER it left your hand.

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)

The frequencies refer to the sample data collected from a population of interest when performing a hypothesis test comparing two or more population proportions.

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)