How much time (in seconds) does the earth take to rotate through an angle of 135 degrees about its axis?

Options

A. 21600
B. 28800
C. 32400
D. 33600

Answer

To find out how much time the Earth takes to rotate through an angle of 135 degrees about its axis, we can follow these steps:

### Step 1: Determine the total time for a complete rotation
The Earth takes 24 hours to complete a full rotation of 360 degrees.

### Step 2: Convert hours into seconds
Since we need the time in seconds, we convert 24 hours into seconds:
- 1 hour = 60 minutes
- 1 minute = 60 seconds
- Therefore, 24 hours = 24 × 60 × 60 seconds

Calculating this:
\[ 24 \times 60 = 1440 \text{ minutes} \]
\[ 1440 \times 60 = 86400 \text{ seconds} \]

### Step 3: Set up a proportion to find the time for 135 degrees
Now we know that 360 degrees takes 86400 seconds. We can set up a proportion to find out how long 135 degrees takes:
\[ \frac{135 \text{ degrees}}{360 \text{ degrees}} = \frac{x \text{ seconds}}{86400 \text{ seconds}} \]

### Step 4: Solve for x
Cross-multiplying gives us:
\[ 135 \times 86400 = 360 \times x \]
\[ 11664000 = 360x \]
Now, divide both sides by 360 to isolate x:
\[ x = \frac{11664000}{360} \]
Calculating this:
\[ x = 32400 \text{ seconds} \]

### Final Answer
The Earth takes **32,400 seconds** to rotate through an angle of 135 degrees about its axis.

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