The earth makes a complete rotation about its axis in 24h. What angles will it turn in 3h 20 min ?

Options

A. `50^(@)`
B. `120^(@)`
C. `130^(@)`
D. None of these

Answer

To solve the problem of how much angle the Earth turns in 3 hours and 20 minutes, we can follow these steps:

### Step 1: Understand the complete rotation
The Earth makes a complete rotation of 360 degrees in 24 hours.

### Step 2: Convert the time into hours
First, we need to convert 3 hours and 20 minutes into hours. We know that:
- 20 minutes is equal to \( \frac{20}{60} \) hours, which simplifies to \( \frac{1}{3} \) hours.

So, 3 hours and 20 minutes can be expressed as:
\[ 3 + \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3} \text{ hours} \]

### Step 3: Calculate the angle turned in that time
Now, we can find out how many degrees the Earth turns in \( \frac{10}{3} \) hours. We can set up a proportion based on the complete rotation:
\[ \text{Angle turned} = \left( \frac{10}{3} \text{ hours} \right) \times \left( \frac{360 \text{ degrees}}{24 \text{ hours}} \right) \]

### Step 4: Simplify the calculation
Now we can simplify this:
\[ \text{Angle turned} = \frac{10}{3} \times \frac{360}{24} \]

Calculating \( \frac{360}{24} \):
\[ \frac{360}{24} = 15 \]
So, we can rewrite the equation as:
\[ \text{Angle turned} = \frac{10}{3} \times 15 \]

### Step 5: Final calculation
Now, multiply:
\[ \text{Angle turned} = \frac{10 \times 15}{3} = \frac{150}{3} = 50 \text{ degrees} \]

### Conclusion
Thus, the Earth turns 50 degrees in 3 hours and 20 minutes.

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