3. (1) The three vectors in Fig. 3 32 can be added in six different orders (V, + V: + V. V. + V, + V, etc.).
Show on a diagram that the same resultant is ob.
tained no matter what the order.

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.

Critical mass is the of material required to produce a chain reaction. a.) minimum amount b.) atomic mass c.) precise amount d.) maximum amount

Diamond will scratch quartz. true or false