EXERC ISE 4.13 An experimental rocket plane lands on skids on a dry lake bed. It's traveling at 80.0m/s when it touches down, how far before coming to rest?Assume the coefficient of kinetic friction between the skids and the lake bed is 0 ,600. ANSW ER 344m

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EXERC ISE 4.13 An experimental rocket plane lands on skids on a dry lake bed. It's traveling at 80.0m/s when it touches down, how far before coming to rest?Assume the coefficient of kinetic friction between the skids and the lake bed is 0 ,600. ANSW ER 344m

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Answer 1

To solve this problem, we need to use the principles of physics, specifically the equations of motion and friction. Here's a step-by-step explanation:

1. Identify the given data:
- Initial velocity (\(v_0\)) = 80.0 m/s
- Final velocity (\(v\))0 m/s (since the plane comes to rest)
- Coefficient of kinetic friction (\(\mu_k\)) = 0.600
- Acceleration due to gravity (\(g\)) = 9.8 m/s² (standard value)

2. Determine the force of kinetic friction:
The force of kinetic friction (\(F_k\)) can be calculated using the formula:
\[
F_k = \mu_k \cdot N
\]
where \(N\) is the normal force. On a flat surface, the normal force is equal to the weight of the object, which is \(mg\).

3. Calculate the deceleration:
The deceleration (\(a\)) due to kinetic friction is given by:
\[
a = \frac{F_k}{ = \frac{\mu_k \cdot mg}{m} = \mu_k \cdot g
\]
Substituting the values:
\[
a = 0.600 \times 9.8 = 5.88 \, \text{m/s}^2
\]

4. Use the kinematic equation to find the stopping distance:
We use the kinematic equation that relates initial velocity, final velocity, acceleration, and distance:
\[
v^2 = v_0^2 + 2ad
\]
Since the final velocity \(v\) is 0, we can rearrange the equation to solve for \(d\) (the stopping distance):
\[
0 = (80.0)^2 + 2(-5.88)d
\]
\[
0 = 6400 - 11.76d
\]
\[
11.76d = 6400
\]
\[
d = \frac{6400}{11.76} \approx 544.2 \, \text{m}
\]

It appears there might be a discrepancy in the provided answer (344 m) versus the calculated answer (544.2 m). Based on the given data and standard physics formulas, the correct stopping distance should be approximately 544.2 meters.

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EXERC ISE 4.13 An experimental rocket plane lands on skids on a dry lake bed. It's traveling at 80.0m/s when it touches down, how far before coming to rest?Assume the coefficient of kinetic friction between the skids and the lake bed is 0 ,600. ANSW ER 344m

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