Two particles travel along the space curves r1(t) = t, t2, t3 r2(t) = 1 + 4t, 1 + 16t, 1 + 52t . find the points at which their paths intersect. (if an answer does not exist, enter dne.) (x, y, z) = (smaller x-value) (x, y, z) = (larger x-value) find the time(s) when the particles collide. (enter your answers as a comma-separated list. if an answer does not exist, enter dne.) t =

This question is worth 54 points ! rock falls from a ledge to the ground what energy conversion occurs during this process a potential to kinetic b kinetic to potential c thermal to mechanical d chemical to mechanical

1. jay fills a wagon with sand (about 20 kg) and pulls it with a rope 30 m along the beach. he holds the rope 25° above the horizontal. the rope exerts a 20-n tension force on the wagon. how much work does the rope do on the wagon?

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.