A rope hanging through a hole

A rope of mass, M and length L lies on a frictionless table, with a short portion, Lo, hanging through the hole. The rope is initially at rest. a) Find a general equation for x(t), the length of the rope throught the hole. b)Evaluate the constants A and B so that the intial conditions are satisfied.

Water shot out of fire hydrant

Water shoots out of a fire hydrant having nozzle diameter D wiht nozzle speed Vo. What is the reaction force on the hydrant?

Rocket terminal velocity

A rocket ascends from rest in a uniform gravitational field by ejecting exhaust with constant speed u. Assume that the rae at which mass is expelled is given by dm/dt=ym, where m is the instantaneous mass of the rocket and y is a constant, and that the rocket is retarded by air resistance with a force of mbv, where b is a constant. Find the velocity of the rocket as a function of time.

Calculating the tension of a rope that is attached to a block.

A uniform rope of mass m and length l is attached to a block of mass M. The rope is pulled with force, F. Find the tension at distance x from the end of the rope. Neglect gravity.

Working with uniform acceleration and the collision point between two players.

There are two football players standing 48 meters apart (player A and player B). They start running towards each other. Player A acceleration is 0.5 m/s2 and player B acceleration is 0.3 m/s2. How much time passes before each player collides with each other? When they collide how far has the first player(player A) traveled?