4.31 A particle of mass m can move on a rough horizontal table and is attached to a fixed point on the table by a light inextensible string of length b. The resistance force exerted on the particle is -mKv, where v is the velocity of the particle. Initially the string is taut and the particle is projected horizontally, at right angles to the string, with speed u. Find the angle turned through by the string before the particle comes to rest. Find also the tension in the string at time t.

Problem 4: Starting from the origin at time t = 0, a particle is given an initial velocity vo along the +x axis. The particle's motion can be described by v(x) = vo(1kx)¹/3 where k is a positive constant. (a) Determine the retarding force F(v) as a function of velocity. [Note: Don't write your final answer in the form F(x, v)! You know v(r), so make sure your expression contains no explicit dependence on z.] (b) Determine x(t), the position of the particle as a function of time. (c) Find the time and place where the particle comes instantaneously to rest, tƒ and xƒ. For each part, check your result for dimensional consistency and limiting-case behavior.

The engine of a model rocket is rated with a total impulse of 5.50 N·s and a thrust duration of 1.10 s. What is the average force exerted by the engine?

A particle of mass m moves down the inner surface of a hemisphere without friction. Find the equations of motion.