A child goes down a playground slide that is inclined at an angle of 24.5° below the horizontal. Find the acceleration of the child given that the coefficient of kinetic friction between the child and the slide is 0.305.

To find the acceleration of the child going down the slide, we need to consider the forces acting on the child.

First, let's define our coordinate system. We'll consider positive x-direction as pointing downwards along the slide and negative y-direction pointing perpendicular to the slide.

The forces acting on the child are:
1. Force of gravity (mg), pointing straight downwards.
2. Normal force (N) exerted by the slide, perpendicular to the slide.
3. Frictional force (f) opposing the child's motion, parallel to the slide.

The force of gravity can be split into two components:
- Component along the slide (mg sin θ), which contributes to the child's acceleration.
- Component perpendicular to the slide (mg cos θ), which cancels out the normal force.

Since the child is moving down the slide, the frictional force is opposing the child's motion, which means it acts in the positive x-direction.

Using Newton's second law (F = ma), we can set up our equations of motion:

Sum of forces in the x-direction:
f = ma

Sum of forces in the y-direction:
mg sin θ - N = 0

The normal force (N) can be obtained from the equation:
N = mg cos θ

Substituting this into the y-direction equation, we get:
mg sin θ - mg cos θ = 0

Simplifying, we find:
sin θ = cos θ

Taking the inverse sine of both sides, we get:
θ = 45°

Therefore, the angle of the slide is 45°.

Now, substituting the value of θ and the given values into the x-direction equation, we have:
f = ma
μN = ma
μ(mg cos θ) = ma
μmg cos θ = ma
μg cos θ = a

Substituting the given values into the equation:
μ = 0.305
g = 9.8 m/s^2
θ = 24.5°

We can now calculate the acceleration:
a = (0.305)(9.8)(cos 24.5°)

Using a calculator, we find:
a ≈ 2.39 m/s^2

Therefore, the acceleration of the child going down the slide is approximately 2.39 m/s^2.