A baseball player throws a ball in the air with an initial speed of 50 m/s at an angle of 30 degrees above the horizontal. What is the vertical component of the ball’s initial velocity assuming up is the positive direction?

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)

What are two different ways you could find the value of a? explain these methods.

A100-watt light bulb illuminates a solar cell. the electricity from the solar cell operates a water pump that delivers 1 watt of power. what is the efficiency of the system?