To determine the ratio of the horizontal force acting on the passenger to their weight, we need to find the horizontal force and the passenger's weight separately.

Step 1: Horizontal Force on the Passenger

The horizontal force ($F_{\text{horizontal}}$) on the passenger is calculated using Newton's second law of motion:

$F_{\text{horizontal}} = m \cdot a$

where:

• $m$ is the mass of the passenger (75.9 kg),
• $a$ is the acceleration of the rocket sled (48.7 m/s²).

Thus,

$F_{\text{horizontal}} = 75.9 \, \text{kg} \times 48.7 \, \text{m/s}^2 = 3696.33 \, \text{N}$

Step 2: Weight of the Passenger

The weight ($W$) of the passenger is the force due to gravity, given by:

$W = m \cdot g$

where $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$).

Thus,

$W = 75.9 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 743.82 \, \text{N}$

Step 3: Ratio of Horizontal Force to Weight

The ratio of the horizontal force to the passenger's weight is:

$\text{Ratio} = \frac{F_{\text{horizontal}}}{W} = \frac{3696.33 \, \text{N}}{743.82 \, \text{N}} \approx 4.97$

Final Answer:

The ratio of the horizontal force to the passenger's weight is approximately 4.97 (dimensionless).

---

Would you like more details or have any questions about this solution?

Here are five related questions for further exploration:

1. How would the ratio change if the acceleration of the sled were doubled?
2. What would be the effect on the ratio if the passenger's mass were halved?
3. How would air resistance affect the actual force experienced by the passenger?
4. What is the significance of the ratio being dimensionless in this context?
5. How would the ratio change on a different planet where gravitational acceleration is different?

Tip: The force of gravity on an object depends on its mass and the local gravitational field, but the horizontal force depends on the object's acceleration and mass. Understanding both is crucial when dealing with forces in multiple directions.