A 60 kg ice skater holds up a large sheet of cardboard that can catch the wind and drive her (frictionlessly) across the ice. While she's moving at 0.5 m/s, a wind that is constant and horizontal for 5.0 s exerts a force on the cardboard of 1.7 N. What is the skater's initial acceleration once the wind begins to blow?

a = F/m

To determine the skater's initial acceleration once the wind begins to blow, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a).

In this case, we are given the force exerted by the wind on the cardboard (F = 1.7 N) and the mass of the skater (m = 60 kg). We need to find the skater's acceleration (a) when the wind starts blowing.

Since the skater is moving at a constant velocity of 0.5 m/s before the wind starts blowing, we can assume that the net force acting on the skater is zero, as there is no acceleration. Therefore, the force exerted by the wind must also be equal to the force of friction acting in the opposite direction.

Now, let's analyze the forces acting on the skater when the wind begins to blow:

1. Force of friction (Ffr): This force opposes the motion of the skater and is equal to the force exerted by the wind (since 0.5 m/s is a constant velocity).

2. Force due to the wind (Fwind): This force acts in the same direction as the skater's motion and is equal to 1.7 N.

Since the force of friction is equal to the force exerted by the wind, we have:

Ffr = Fwind
Ffr = 1.7 N

Using Newton's second law, we can substitute the mass of the skater for the force of friction:

Ffr = m * a
1.7 N = 60 kg * a

Rearranging the equation to solve for acceleration (a), we have:

a = 1.7 N / 60 kg
a ≈ 0.028 m/s²

Therefore, the skater's initial acceleration once the wind begins to blow is approximately 0.028 m/s².