Astone is tied to a string (length 1.10 m) and whirled in a circle at the same constant speed in two different ways. first, the circle is horizontal and the string is nearly parallel to the ground. next, the cir- cle is vertical. in the vertical case the maximum tension in the string is 15.0% larger than the tension that exists when the circle is horizontal. determine the speed of the stone.'

The mass of a muon is 207 times the electron mass; the average lifetime of muons at rest is 2.21 μs. in a certain experiment, muons moving through a laboratory are measured to have an average lifetime of 7.04 μs. for the moving muons, what are (a) β (b) k, and (c) p? the rest energy of the electron is 0.511 mev.

Aplane flies directly between two cities, a and b, which are separated by . from a to b, the plane flies into a headwind. on the return trip from b to a, the wind velocity is unchanged. the trip from b to a takes less than the trip from a to b. what is the airspeed of the plane, assuming it is the same in both directions

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.)