You are traveling on an airplane. The velocity of the plane with respect to the air is 150 m/s due east. The velocity of the air with respect to the ground is 38 m/s at an angle of 30° west of due north.

The focal length of a relaxed human eye is approximately 1.7 cm. when we focus our eyes on a close up object, we can change the refractive power of the eye by about 16 diopters. (a) does the refractive power of our eyes increase or decrease by 16 diopters when we focus closely? explain. (b) calculate the focal length of the eye when we focus closely.

Apebble is thrown into a calm lake, ripples are formed from the center and move outward. the water particles in the lake travel in a circular pattern that moves up and down on the surface of a lake, and the energy travels a) diagonally. b) downward. c) horizontally. d) upward.

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.