To determine the acceleration of the man and the woman, we can use 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. The equation can be written as:
a = F / m
where a is the acceleration, F is the net force, and m is the mass.
(a) To find the acceleration of the man, we'll use his mass, which is 95 kg, and the net force acting on him, which is the force exerted by the woman, equal to 57 N. Since the woman is pushing towards the east, the force will also act towards the east direction. Therefore, we can plug the values into the equation:
a_man = 57 N / 95 kg
Calculating the value will give us the acceleration of the man.
(b) To determine the acceleration of the woman, we'll use the same equation. However, the net force acting on the woman is the reaction force from the man, which will have the same magnitude but act in the opposite direction. So the force acting on the woman will also be 57 N, but it will be directed towards the west. Plugging the values into the equation:
a_woman = 57 N / 55 kg
Calculating the value will provide the acceleration of the woman.
Note: The acceleration is a scalar value representing its magnitude, but since the forces and resulting accelerations are in opposite directions for the man and the woman, the directions will be opposite as well.