The rocket sled shown in the figure accelerates towards the right at a rate of 48.7m/s2
. Its passenger has a mass of 75.9kg
. Part (b)   
What is the ratio of horizontal force to the passenger's weight? Your answer is a dimensionless ratio. 

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).

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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.

The rocket sled shown in the figure accelerates towards the right at a rate of 48.7 m/s². Its passenger has a mass of 75.9 kg. Part (b) What is the ratio of horizontal force to the passenger's weight? Your answer is a dimensionless ratio.

Learn how to calculate the ratio of the horizontal force to the passenger's weight in a rocket sled accelerating at 48.7 m/s². This step-by-step solution covers Newton's Second Law and weight calculation. Ideal for students in Grades 9-12.

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