Two smooth spheres of equal radii and with masses 2m, 5m are on a horizontal table. the sphere of mass 2m, travelling with speed 3u, collides directly with the sphere of mass 5m, which is traveling with speed u in the same direction. the coefficient of elasticity between the spheres is e 1/4 (i) (5 points) find the speed and direction of each ball after the collision. ii) (5 points) find an expression, involving m and u, for the kinetic energy lost in the collision. (b) (10 points) examine whether or not the following system of forces is in equilib- rium + 5k acting at (-7,5,-5) f2 = 21-j-k acting at(-2,4,-19) fa ij-6ok acting at (-1,2,-2)

"an open tank has the shape of a right circular cone. the tank is 6 feet across the top and 5 feet high. how much work is done in emptying the tank by pumping the water over the top edge? note: the density of water is 62.4 lbs per cubic foot."

A2k pendulum has a speed of 1 m/s at a height of 1/2 meter

Your starship, the aimless wanderer, lands on the mysterious planet mongo. as chief scientist-engineer, you make the following measurements: a 2.50-kg stone thrown upward from the ground at 14.0 m/s returns to the ground in 5.70 s ; the circumference of mongo at the equator is 2.20×10^5 km ; and there is no appreciable atmosphere on mongo. (a) the starship commander, captain confusion, asks for the following information: what is the mass of mongo? (b) if the aimless wanderer goes into a circular orbit 2.20×10^4 km above the surface of mongo, how many hours will it take the ship to complete one orbit? (c) an unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 44.0 km . to the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed of the spacecraft by 23.0 m/s . if nothing is done to correct its orbit, with what speed (in km/h) will the spacecraft crash into the lunar surface?