**Problem 1:**

A 90 kg fullback running east with a speed of 5 m/s is tackled by a 95 kg opponent running north with a speed of 3 m/s. If the collision is perfectly inelastic, calculate the speed and the direction of the players just after the tackle.

**Problem 2:**

A ball of mass M on a frictionless horizontal table is pulled by a constant
horizontal force F. A coiled up rope of mass per unit length r is attached
which uncoils as the body moves.

(a) By taking into account the
uncoiling of the rope, derive an expression for the speed of the ball as a
function of distance traveled.

(b) Evaluate the terminal speed of the
ball, assuming a very long rope.

**Problem 3:**

Three elastic spheres of equal size are suspended on^{ }light strings
as shown; the spheres nearly touch each other.^{ }The mass M of the
middle sphere is unknown; the^{ }masses of the other two spheres are 4m
and m.^{ }The sphere of mass 4m is pulled sideways until it is elevated
a distance h from its equilibrium position and then released. What must the
mass of the middle sphere be in order for the sphere of mass m to rise to a^{
}maximum possible elevation after the first collision with the middle
sphere? What is that maximum elevation H?

**Problem 4:**

A light flat ribbon is placed over the top of a triangular prism as shown in
the diagram. Two blocks are placed on the ribbon. The coefficients of static
and kinetic friction between the ribbon and the blocks are μ_{s} and μ_{k},
respectively. There is no friction between the ribbon and the prism. The angle
θ and the masses of the blocks m and M are given. Assuming that M > m, find the
acceleration of the ribbon along the prism after the blocks are simultaneously
released. Consider all possible cases.

**Problem 5:**

A rocket of initial mass m_{0} ejects fuel at a constant rate km_{0}
and at a velocity v' relative to the rocket shell of mass m_{1}.

(a) Show that the minimum rate of fuel consumption that will allow the rocket to
rise at once is k = g/v' where g is the gravitational acceleration.

(b) Find
the greatest speed achieved and the greatest height reached under that
condition.