The potential energy of a catapult was completely converted into kinetic energy by releasing a small stone with a mass of 20 grams. The velocity of the stone when it reached the target was 15.0 meters/second. What was the value of the kinetic energy of the stone when it reached the target?

Let f(x) = x4- 8x2 . find the relativeextrema of this function using the second derivative test.

An object is 10 cm from the mirror, its height is 1 cm and the focal length is 5 cm. what is the image height? (indicate the object orientation by including the + or - sign with the answer.) hi = cm +1 -1 +10 -10

Consider a one meter long horizontal pipe with a constant 100 cm^2 cross sectional area. water flows rightward into the pipe at x = 0 with flow velocity 02m/sec at every point within the pipe intake area. at x=1, the rightward flow rate is 0.192 m/sec. assume the water is a conserved quantity in the pipe, so there must be a leak (a sink) somewhere in the pipe. 1. compute net volumetric flow of the source if the system to be in equilibrium. 2. now assume the pipe in the problem has no leaks. compute the net volumetric rate of change for the system.