A cougar is crouched on the branch of a tree that is 3.82 m above the ground. He sees an unsuspecting rabbit on the ground, sitting 4.12 m from the spot directly below the branch on which he is crouched. He jumps horizontally and lands on the rabbit. (a) How long was the cougar in flight? (b) What was the initial velocity of the cougar?

Ahot-air balloon is drifting straight downward with a constant speed of 2.40 m/s. when the balloon is 7.63 m above the ground, the balloonist decides to drop one of the ballast sandbags to the ground below. how much time elapses before the sandbag hits the ground?

The consumption of fossil fuels could be

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.)