Two skaters, a man and a woman, are standing on ice. Neglect any friction between the skate blades and the ice. The mass of the man is 81 kg, and the mass of the woman is 60 kg. The woman pushes on the man with a force of 50 N due east. Determine the acceleration (magnitude and direction) of (a) the man and (b) the woman.

F = m a

a of man = 50/81 east
a of woman = 50/60 west

To determine the acceleration of the man and the woman, we need to apply Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

a) Let's start by finding the acceleration of the man. The net force acting on him is the force exerted by the woman:

Net Force on Man = Force exerted by Woman = 50 N (due east)

Since the woman is pushing the man, the force is applied in the eastward direction. Therefore, the acceleration of the man will also be in the eastward direction.

Using Newton's second law:

Net Force = Mass * Acceleration

Rearranging the equation:

Acceleration = Net Force / Mass

Plugging in the known values:

Acceleration of the Man = 50 N / 81 kg

Using a calculator, we find that the acceleration of the man is approximately 0.617 m/s² (eastward).

b) Now, let's find the acceleration of the woman. According to Newton's third law of motion, every action has an equal and opposite reaction. So, the force exerted by the woman on the man will also be felt by the woman but in the opposite direction (westward).

Net Force on Woman = Force exerted by the Woman = -50 N (due west)

Since the force is applied in the westward direction, the acceleration of the woman will also be in the westward direction.

Using Newton's second law:

Net Force = Mass * Acceleration

Rearranging the equation:

Acceleration = Net Force / Mass

Plugging in the known values:

Acceleration of the Woman = -50 N / 60 kg

Since the force is in the opposite direction, we use a negative sign in the calculation. Using a calculator, we find that the acceleration of the woman is approximately -0.833 m/s² (westward).