An arrow is shot horizontally from the top of a building and it lands 200m from the foot of the building after 10 seconds. Assuming air resistance is negligeble, Calculate initial velocity and the height of the building

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.

Because light travels in a straight line and casts a shadow, isaac newton hypothesized that light is

What is the speed of an object at a given moment?