In some proton accelerators, proton beams are directed toward each other for head-on collisions. Suppose that in such an accelerator, protons move with a speed relative to the lab of 0.9898c.

(a) Calculate the speed of approach of one proton with respect to another one with which it is about to collide head on. Answer given for is .99995c.

(b) What is the kinetic energy of each proton (in units of MeV) in the laboratory reference frame? Answer given is 5640MeV.

(c) What is the kinetic energy of one of the colliding protons (in units of MeV) in the rest frame of the other proton? Answer given is 91500MeV.

Atank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. the values in the table show the volume v of water remaining in the tank (in gallons) after t minutes.t(min) 5 10 15 20 25 30v(gal) 694 444 250 111 28 0(a) if p is the point (15, 250) on the graph of v, find the slopes of the secant lines pq when q is the point on the graph with t = 5, 10, 20, 25, and 30.(b) estimate the slope of the tangent line at p by averaging the slopes of two secant lines.(c) use a graph of the function to estimate the slope of the tangent line at p. (this slope represents the rate at which the water is flowing from the tank after 15 minutes.)show all steps.

Water is siphoned from a large tank and discharges into the atmosphere through a 50-mm diameter tube. the end of the tube is b = 2.1 m below the tank bottom which is a = 7.4 m deep, and viscous effects are negligible. determine the maximum height h over which the water can be siphoned without cavitation occurring. atmospheric pressure is 101.4 kpa, and the water vapor pressure is 1.79 kpa (absolute)

What is the mass of the water that is being heated? it requires 2,500 joules to raise a certain amount of water (c = 4.186 jig c) from 20.0°c to 60.0°c. o 159 o 40 g o 63 g o 80 g