To answer this question, you need to know the definition of Relative Motion:
The motion is relative when it depends on a reference point or referencial system. If you know the reference point, you can determine the velocity of an object.
If you are sitting on your chair, you are not moving relative to it (Your speed is 0 km/s); but as you know, our planet moves around the Sun (Traslation Movement) with a speed of 30.0 km/s. Therefore, you are moving 30.0 km/s relative to the sun.
You have to divide the pressure exerted by the air into two partial pressures: of the dry air and of the water vapor. Combining these two values gives you the parameter.
Newton's second law states that the resultant of the forces applied to an object is equal to the product between the object's mass and its acceleration:

where in our problem, m is the mass the (child+cart) and a is the acceleration of the system.
We are only concerned about what it happens on the horizontal axis, so there are two forces acting on the cart+child system: the force F of the man pushing it, and the frictional force

acting in the opposite direction. So Newton's second law can be rewritten as

or

since the frictional force is 15 N and we want to achieve an acceleration of

, we can substitute these values to find what is the force the man needs: