What is approximately the centripetal acceleration (in units of acceleration due to gravity on earth, g = 10 m `s^(-2)` of an air-craft flying at a speed of 400 m `s^(-1)` through a circular arc of radius 0.6 km ?

Options

A. 26.7
B. 16.9
C. 13.5
D. 30.2

Explanation

To find the centripetal acceleration of the aircraft flying through a circular arc, we can follow these steps:

### Step 1: Identify the given values
- Speed of the aircraft (V) = 400 m/s
- Radius of the circular arc (R) = 0.6 km = 0.6 × 10^3 m = 600 m

### Step 2: Use the formula for centripetal acceleration
The formula for centripetal acceleration (a_c) is given by:
\[ a_c = \frac{V^2}{R} \]

### Step 3: Substitute the values into the formula
Now, substitute the values of V and R into the formula:
\[ a_c = \frac{(400 \, \text{m/s})^2}{600 \, \text{m}} \]

### Step 4: Calculate V^2
Calculate \( V^2 \):
\[ V^2 = 400^2 = 160000 \, \text{m}^2/\text{s}^2 \]

### Step 5: Calculate centripetal acceleration
Now substitute \( V^2 \) into the centripetal acceleration formula:
\[ a_c = \frac{160000 \, \text{m}^2/\text{s}^2}{600 \, \text{m}} \]

### Step 6: Perform the division
Now perform the division:
\[ a_c = \frac{160000}{600} \approx 266.67 \, \text{m/s}^2 \]

### Step 7: Convert to units of g
To express this in terms of acceleration due to gravity (g = 10 m/s²):
\[ \text{Centripetal acceleration in terms of g} = \frac{266.67 \, \text{m/s}^2}{10 \, \text{m/s}^2} \approx 26.67 \, g \]

### Final Answer
Thus, the centripetal acceleration of the aircraft is approximately **26.7 g**.

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