From the top of a 286-foot lighthouse, a plane is sighted overhead, and a ship is observed directly below the plane. the angle of elevation of the plane is 24degrees, and the angle of depression of the ship is 35degrees. find a. the distance of the ship from the lighthouse and b. the plane's height above the water. round to the nearest foot.

Does work output exceed work input when a machine is used? a) yes, it does, as machines create energy. b) it depends on the type of machine used. c) no, it doesn’t, as machines are inefficient. d) no, it doesn’t, as machines cannot create energy.

Suppose while hauling rocks, you accidentally drop one. it breaks apart in flat, planar sections. what type of rock did you just drop? 20 points

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)