A raindrop with initial mass M0 starts falling from rest under the influence of gravity. Assume that the drop gains mass from the cloud at a rate proportional to the product of its instantaneous mass and velocity:dM/dt = k M v where k is a constant. Show that the speed of the drop approaches a constant after a long time, derive an expression for the terminal speed, and calculate the terminal speed. Neglect air resistance.

Asmall blob of putty of mass m falls from the ceiling and lands on the outer rim of a turntable of radius r and moment of inertia i0 that is rotating freely with angular speed ω0 about its vertical fixed-symmetry axis. (use any variable or symbol stated above as necessary.)

Matt is driving down 7th street. he drives 150 meters in 18 sec. assuming he doesn’t slow down or speed up, what is his speed?

Astudent is performing an experiment comparing sound and light waves. the student gathers the following data. what conclusion does the student most likely make based on this data? light waves always travel the same speed; however, the speed of sound is determined by the medium that it travels through. all sound waves always have the same energy, so the temperature of the medium does not affect wave speed. light needs to vibrate particles, so it travels fastest in tightly packed solids, while sound does not need a medium, so it travels fastest in a gas. tightly packed particles in solids slow down the light waves; however, sound waves make particles bounce into each other, so they travel faster in solids.