A red shift of `60 Å` is observed in light of wavelength `5000 Å` coming from a distant red gaint star. Calculate the velocity of the distant nebula.

Answer

To solve the problem of calculating the velocity of a distant nebula based on the observed redshift, we can follow these steps:

### Step 1: Understand the given information
We are given:
- Redshift (Δλ) = 60 Å
- Original wavelength (λ) = 5000 Å

### Step 2: Use the formula for redshift
The relationship between the change in wavelength (Δλ), the original wavelength (λ), and the velocity (V) of the star moving away from us can be expressed as:
\[ \frac{\Delta \lambda}{\lambda} = \frac{V}{C} \]
where:
- \(C\) is the speed of light, approximately \(3 \times 10^8\) m/s.

### Step 3: Substitute the known values into the formula
Substituting the known values into the equation:
\[ \frac{60 \, \text{Å}}{5000 \, \text{Å}} = \frac{V}{3 \times 10^8 \, \text{m/s}} \]

### Step 4: Simplify the left side of the equation
Calculating the left side:
\[ \frac{60}{5000} = 0.012 \]
So, the equation now looks like:
\[ 0.012 = \frac{V}{3 \times 10^8} \]

### Step 5: Solve for V
Now, we can solve for \(V\):
\[ V = 0.012 \times 3 \times 10^8 \]
Calculating this gives:
\[ V = 3.6 \times 10^6 \, \text{m/s} \]

### Step 6: Interpret the result
The positive value of \(V\) indicates that the nebula is moving away from us, consistent with the redshift observed.

### Final Answer
The velocity of the distant nebula is \(3.6 \times 10^6 \, \text{m/s}\).

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