Determine mass flow rate and velocity of efflux from circular hole of 0.1 diameter at the bottom of water tank at this instant . The tank is open to atmosphere and H=4m

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.

Ablock of mass 1.5 kg slides down an inclined plane that has an angle of 15. if the inclined plane has no friction and the block starts at a height of 3 m, how much kinetic energy does the block have when it reaches the bottom? acceleration due to gravity is g = 9.8 m/s2. a. 6.8 j b. 50.9 j c. 0 j d. 44.1 j

At time t=0, a particle is located at the point (3,6,9). it travels in a straight line to the point (5,2,7), has speed 8 at (3,6,9) and constant acceleration 2i−4j−2k. find an equation for the position vector of the particle.