Projectile problem

A hunter aim directly at a target (on the same level) 120 meters away. If the bullet leaves the gun at a speed of 250m/sec, by how much will it miss the target? At what angle should the gun be aimed so the target will be hit?

Calculating the total time and the average force during the movement of a mass on a surface.

On a frictionless ice a variable force P in Newtons, expressed by P= 5 + 6 t, is applied to an initially stationary block of wood to move it across the ice until its final speed is V= 25 m/sec. The mass of the wood is M= 3 kg. Vectors P and V are in the same direction. a. Find the time, in seconds, that the force is applied. b. Find the average force during the force application.

Calculating the loss of mechanical energy.

A block of mass M slides along a horizontal table with speed Vo. At x=0 it hits a spring constant k and begins to experience a frictional force. The coefficient of friction is a variable and is given by u=bx, where b is a constant. Find the loss in mechanical energy when the block has come momentarily to rest.

Mass moving in circular motion

Mass m whirls on a frictionless table, held to circular motion by a string which passes through a hole in that table. The string is slowly pulled through the hole so that the radius of the circle changes from L1 to L2. Show that the work done in pulling the string equals the increase in kinectic energy.

Calculating a leaping man's power.

A 160 lb man leaps into the air from a crouching position. His center of gravity rises 1.5 ft before he leaves the ground, and it then rises 3 ft to the top of his leap. What power does he develop assuming that he pushes the ground with constant force?