The distance between the point slip and the nose of the obtuse crossing can be determined using the given switch angle, diamond angle, and radius of slip. Let's break down the solution into steps:

Step 1: Understanding the problem
- The switch angle is the angle between the diverging track and the straight track.
- The diamond angle is the angle between the straight track and the crossing diamond.
- The radius of slip is the radius of the curve formed by the diverging track.

Step 2: Calculate the tangent angle
- The tangent angle is the angle formed between the diverging track and the radius of slip.
- It can be calculated using the formula: tangent angle = switch angle - diamond angle.
- Substituting the given values, tangent angle = 75° - 45° = 30°.

Step 3: Calculate the distance between the slip and the obtuse crossing
- The distance between the slip and the obtuse crossing can be calculated using the formula: distance = radius of slip * tan(tangent angle).
- Substituting the given values, distance = 38 m * tan(30°).
- Using a scientific calculator, tan(30°) is approximately 0.57735.
- Therefore, distance = 38 m * 0.57735 ≈ 21.92 m.

Step 4: Calculate the distance between the slip and the nose of the obtuse crossing
- The distance between the slip and the nose of the obtuse crossing can be calculated by subtracting the distance between the slip and the obtuse crossing from the radius of slip.
- Distance between the slip and the nose of the obtuse crossing = radius of slip - distance.
- Substituting the calculated value, distance = 38 m - 21.92 m ≈ 16.08 m.

Step 5: Convert the distance to two decimal places
- Rounding off the distance to two decimal places, the final answer is approximately 16.08 m ≈ 16.09 m.

Therefore, the distance between the point slip and the nose of the obtuse crossing is approximately 16.09 m.

Given: S = 75^o, ∝ = 45^o and r = 38 m