You are at the controls of a particle accelerator, sending a beam of 1.80 x 10^7 m/s protons (mass m) at a gas target of an unknown element. Your detector tells you that some protons bounce straight back after a collision with one of the nuclei of the unknown element. All such protons rebound with a speed of 1.50 x 10^7 m/s . Assume that the initial speed of the target nucleus is negligible and the collision is elastic.
(a) Find the mass of one of the nuclei of the unknown element. Express you answer in terms of the proton mass m.
(b) What is the speed of the unknown nucleus immediately after such a collision?

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.

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

The volume of a gas is halved during an adiabatic compression that increases the pressure by a factor of 2.5. what is the specific heat ratio? show the math steps .