How does the speed of a wave relate to its wavelength and frequency?*

You and a friend (alex) are at a a tree-top adventure park .. . part of the course requires you to climb up a rope. you both climb the same rope in the same amount of time. however, the tension in the rope is greater when alex climbs. who did the most work? alex did - more tension means more force - more force means more work was done you did - less tension means less force - less force means more work was done to find the work done, the force exerted and distance moved are multiplied. a couch is moved twice before you are happy with its placement. the same force was used to move the couch both times. if more work is done the first time it is moved, what do you know about the distance it was moved? when more work was done, the couch was moved less. when more work was done, the couch was moved further. when more work was done, the couch wasn't moved at all. when more work was done, the couch was moved the same distance.

Two steel balls, each of mass m, are welded to a light rod of length l and negligible mass and are initially at rest on a smooth horizontal surface. a horizontal force of magnitude f is suddenly applied to the rod as shown. determine (a) the instantaneous acceleration a of the mass center g and (b) the corresponding rate at which the angular velocity of the assembly about g is changing with time.

Engines for propeller-driven aircraft are limited in their maximum rotational speed by the fact that the tip speed of the propeller must not approach the speed of sound in air (mach i). taking 6 ft as a typical diameter for a propeller of a light airplane and 1100 fils as the speed of sound, find the upper limit on the rpm (revolutions per minute) of the propeller shaft.