Asoftball is hit over a third baseman's head with some speed v0 at an angle θ above the horizontal. immediately after the ball is hit, the third baseman turns around and begins to run at a constant velocity v=7.00m/s. he catches the ball t=2.00s later at the same height at which it left the bat. the third baseman was originally standing l=18.0m from the location at which the ball was hit.

a) find v0. use g=9.81m/s2 for the magnitude of the acceleration due to gravity.

express the initial speed numerically in units of meters per second to three significant figures.

b) find the angle θ in degrees.

express your answer numerically in degrees to three significant figures.

The key to stability is feedback between the reservoir and the fluxes into and/or out of the reservoir. assume that the rate of outflow from a reservoir depends on the size of the reservoir according to the following relationship: outflow rate= k x (size of reservoir), where k is a constant. a reservoir of water has a volume of 5000 liters, and the rate of outflow at steady state is 25 liters per minute. what is k? (give both the numerical value and its units.) what is the residence time? what is the relationship between k and the residence time?

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)

The three classes of rocks are sedimentary, metamorphic, and igneous. how are rocks classified into one of these three groups?