Water leaks out of a 3,200-gallon storage tank (initially full) at the rate v '(t) = 80 -t, where t is measured in hours and v in gallons. a. how much water leaked out between 10 and 20 hours? b. how long will it take the tank to drain completely?

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

An object has a weight of 500 on earth what is the mass of this object

What is required for an electric charge to flow through a wire? zero resistance in the wire a balance of electric potential high resistance in the wire a difference in electric potential