(a) Each experiences an acceleration that has a different magnitude.
(d) Each experiences a pushing force that has the same magnitude.
Explanation:
We start by analyzing the problem using Newton's third law, which states that:
"When an object A exerts a force (called action) on an object B, then object B exerts an equal and opposite force (called reaction) on object A"
Here we can identify the father as object A and the daughter as object B: this means that according to this law, the force exerted by the father on the daughter is equal in magnitude (and opposite in direction) to the force exerted by the daughter on the father.
So, the statement
(d) Each experiences a pushing force that has the same magnitude.
is correct.
Now we analyze the acceleration of each. Acceleration can be found by using Newton's second law:
[tex]a=\frac{F}{m}[/tex]
where
a is the acceleration
F is the force exerted on the body
m is the mass of the body
We notice that for equal forces, the acceleration of a body is inversely proportional to its mass, [tex]a\propto \frac{1}{m}[/tex]. In this problem, we said that the force exerted on the father and on the daughter are equal, but their masses are not (the father has a larger mass): this means, therefore, that the acceleration of the father will be smaller compared to the acceleration of the daughter.
So, the statement
(a) Each experiences an acceleration that has a different magnitude.
is also correct.
Learn more about Newton laws of motion:
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