Two objects (m1 = 4.90 kg and m2 = 2.75 kg) are connected by a light string passing over a light, frictionless pulley as in the figure below. The 4.90-kg object is released from rest at a point h = 4.00 m above the table.

(a) Determine the speed of each object when the two pass each other.
m/s

(b) Determine the speed of each object at the moment the 4.90-kg object hits the table.
m/s

(c) How much higher does the 2.75-kg object travel after the 4.90-kg object hits the table?
m

To solve this problem, we can use the principle of conservation of mechanical energy. First, let's define the relevant quantities:

m1 = mass of the 4.90 kg object
m2 = mass of the 2.75 kg object
h = initial height of the 4.90 kg object
v1 = speed of the 4.90 kg object when they pass each other
v2 = speed of the 2.75 kg object when they pass each other
ht = height from which the 4.90 kg object falls to the table
vf1 = final velocity of the 4.90 kg object when it hits the table
vf2 = final velocity of the 2.75 kg object when it hits the table
d = distance traveled by the 2.75 kg object after the 4.90 kg object hits the table

(a) To determine the speed of each object when they pass each other, we can equate the potential energy lost by the 4.90 kg object to the kinetic energy gained by the 2.75 kg object.
m1 * g * h = (1/2) * m1 * v1^2 + (1/2) * m2 * v2^2

(b) To determine the speed of each object at the moment the 4.90 kg object hits the table, we can again use the conservation of mechanical energy. This time, we need to consider the potential energy lost by the 4.90 kg object and the potential energy gained by the 2.75 kg object when it gets lifted up.
m1 * g * h = (1/2) * m1 * vf1^2 + m2 * g * (h - ht) + (1/2) * m2 * vf2^2, where ht = h - vf1^2 / (2 * g)

(c) To calculate how much higher the 2.75 kg object travels after the 4.90 kg object hits the table, we can determine the initial speed of the 2.75 kg object after they pass each other and then use conservation of mechanical energy again.
m1 * g * h = (1/2) * m1 * v1^2 + m2 * g * d + (1/2) * m2 * vf2^2

Solving the system of equations formed by these equations, we can find the values of v1, v2, vf1, vf2, and d.