A conveyor belt moves to the right with speed v=300 m/min. A pieman puts pies on the belt at a rate of 20 per minute while walking with speed 30 m/min towards a receiver at the other end. The frequency with which they are received by the stationary receiver is

Options

A. 26.67 / min
B. 30/ min
C. 22.22 / min
D. 24 / min

Answer

To solve the problem step by step, we need to analyze the situation involving the conveyor belt, the pieman, and the stationary receiver.

### Step 1: Identify the given values
- Speed of the conveyor belt (V) = 300 m/min
- Rate at which pies are placed on the belt (f) = 20 pies/min
- Speed of the pieman (Vs) = 30 m/min

### Step 2: Understand the scenario
The pieman is walking towards the receiver while placing pies on the conveyor belt. The conveyor belt is also moving, which means the pies will reach the receiver at a different frequency than they are placed on the belt.

### Step 3: Use the formula for apparent frequency
In this scenario, we can use the formula for apparent frequency (f') in the context of the Doppler effect:
\[ f' = f \times \frac{V}{V - Vs} \]
where:
- \( f' \) = apparent frequency (frequency at which pies are received)
- \( f \) = actual frequency (20 pies/min)
- \( V \) = speed of the conveyor belt (300 m/min)
- \( Vs \) = speed of the pieman (30 m/min)

### Step 4: Substitute the values into the formula
Now, we substitute the known values into the formula:
\[ f' = 20 \times \frac{300}{300 - 30} \]

### Step 5: Simplify the equation
Calculate the denominator:
\[ 300 - 30 = 270 \]
Now substitute this back into the equation:
\[ f' = 20 \times \frac{300}{270} \]

### Step 6: Calculate the apparent frequency
Now perform the multiplication and division:
\[ f' = 20 \times \frac{300}{270} = 20 \times 1.1111 \approx 22.22 \text{ pies/min} \]

### Final Answer
The frequency with which the pies are received by the stationary receiver is approximately **22.22 pies/min**.

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