Question

a mother and daughter press their hands together and then push apart while ice skating. immediately after they push away from each other, how does the motion of the mother and daughter change? a. the mother moves forward, and the daughter moves backward with greater acceleration. b. both move forward, but the mother moves with greater acceleration. c. the mother moves backward, and the daughter moves forward with a greater acceleration. d. both move backward, but the daughter moves with greater acceleration. (image: mother labeled 100 kg, daughter labeled 50 kg, with 15n force arrows between them on ice skates)

Explanation:

1. Newton's Third Law: When the mother and daughter push each other, they exert equal and opposite forces (action - reaction pair). So the force on the mother (\(F_m\)) and the force on the daughter (\(F_d\)) have the same magnitude (\(F_m = F_d=15\space N\)) but opposite directions.
2. Newton's Second Law (\(F = ma\)): We can solve for acceleration \(a=\frac{F}{m}\). The mass of the mother (\(m_m = 100\space kg\)) and the mass of the daughter (\(m_d=50\space kg\)).

• For the mother: \(a_m=\frac{F_m}{m_m}=\frac{15}{100} = 0.15\space m/s^2\) (direction opposite to the force she exerts, so if the daughter pushes her with a force, the mother moves backward).
• For the daughter: \(a_d=\frac{F_d}{m_d}=\frac{15}{50}=0.3\space m/s^2\) (direction opposite to the force she exerts, so if the mother pushes her with a force, the daughter moves forward). Since \(a_d>a_m\), the daughter moves with greater acceleration.

Answer:

C. The mother moves backward, and the daughter moves forward with a greater acceleration.