What would the radius (in mm) of the Earth have to be in order for the escape speed of the Earth to equal the speed of light (3 x 108 m/s)? You may ignore all other gravitational interactions for the rocket and assume that the Earth-rocket system is isolated.

Molten iron fills a mould, which has a volume of 200 cm cubed. calculate the volume when the iron cools and solidifies.

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.

Write the function getkthdigit(n, k) that takes a possibly-negative int n and a non-negative int k, and returns the kth digit of n, starting from 0, counting from the right