Romeo takes a uniform 15.0-m ladder and leans it against the smooth (frictionless) wall of the Capulet residence. The ladder's mass is 20.2 kg and the bottom rests on the ground 3.07 m from the wall. When Romeo, whose mass is 70 kg, gets 93.2 percent of the way to the top, the ladder begins to slip. What is the coefficient of static friction between the ground and the ladder?

To determine the coefficient of static friction between the ground and the ladder, we need to analyze the forces acting on the ladder and apply Newton's laws of motion. Here are the steps to find the answer:

1. Identify the forces acting on the ladder:
- Weight force (Wl) acting downwards at the center of mass of the ladder (assume g = 9.8 m/s^2)
- Normal force (N) exerted by the ground on the ladder perpendicular to the surface.
- Frictional force (Fs) opposing the sliding motion parallel to the surface of the ground.
- Tension force (T) acting upwards along the ladder due to Romeo's weight.

2. Determine the weight force (Wl) of the ladder:
Wl = m*ladder*g
= 20.2 kg * 9.8 m/s^2
= 198.76 N

3. Calculate the normal force (N) exerted by the ground:
Since the ladder is not accelerating vertically, N must equal Wl:
N = Wl
= 198.76 N

4. Determine the tension force (T) in the ladder:
T = m*Romeo*g
= 70 kg * 9.8 m/s^2
= 686 N

5. Draw a free-body diagram of the ladder at the point where it starts slipping:
- The normal force (N) acts perpendicular to the ground.
- The frictional force (Fs) acts parallel to the ground and opposes the motion of the ladder.
- The tension force (T) acts vertically upwards.
- The weight force (Wl) acts downward at the center of mass of the ladder.

6. Apply Newton's second law in the horizontal (x-axis) direction:
The sum of the horizontal forces equals zero since the ladder is not accelerating horizontally.
Fs = T * sinθ
= 686 N * sinθ

7. Apply Newton's second law in the vertical (y-axis) direction:
The sum of the vertical forces equals zero since the ladder is not accelerating vertically.
N - Wl - T * cosθ = 0
N = Wl + T * cosθ
= 198.76 N + 686 N * cosθ

8. Substitute N from step 4 into the equation from step 7 and solve for cosθ:
198.76 N + 686 N * cosθ - Wl = 0
cosθ = (Wl - 198.76 N) / 686 N

9. Calculate the angle θ using cosine inverse:
θ = cos^(-1) ((Wl - 198.76 N) / 686 N)

10. Determine the coefficient of static friction (μs) using the following formula:
μs = Fs / N
= (686 N * sinθ) / 198.76 N

11. Calculate the coefficient of static friction (μs):
μs = (686 N * sinθ) / 198.76 N

Now, substitute the calculated values of θ in the equation from step 11 to obtain the coefficient of static friction between the ground and the ladder.