An 86 kg student is sitting in a rolling chair. To roll towards the trash can to throw away
her trash she throws her 27 kg backpack away from her at 6 m/s. What velocity will the
student roll away with?

Which is the best for showing percentages of different types of cars sold(gas hybrid , electric , other ) in the united states ?

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.

Unpolarized light of intensity i_0=750w/m^2 is incident upon two polarizers. after passing through both polarizers the intensity is i_2=280w/m^2. (a) what is the intensity of the light after it passes through the first polarizer in w/m^2? (b) write an equation for the angle between the polarizers in terms of the initial (i_0) and final (i_2) intensities. (c) find the angle between the polarizers in degrees.