A train moves in north direction with a speed of 54 km/hr. and a monkey running on the roof of the train, against its motion with a velocity of 18km/hr. with respect to the train, then the velocity of monkey as observed by a man standing on the ground:-

Options

A. `5 ms^(-1)` due south
B. `25 ms^(-1)` due south
C. `10 ms^(-1)` due south
D. `10 ms^(-1)` due north

Explanation

To solve the problem of determining the velocity of the monkey as observed by a man standing on the ground, we can follow these steps:

### Step 1: Understand the velocities involved
- The train is moving north with a speed of 54 km/hr.
- The monkey is running against the motion of the train with a speed of 18 km/hr relative to the train.

### Step 2: Define the direction of motion
- Since the train is moving north, we can define the north direction as positive.
- The monkey is running against the train's motion, which means its velocity relative to the train will be negative.

### Step 3: Assign values to the velocities
- Velocity of the train (V_train) = +54 km/hr (north)
- Velocity of the monkey with respect to the train (V_monkey/train) = -18 km/hr (against the motion)

### Step 4: Calculate the velocity of the monkey with respect to the ground
To find the velocity of the monkey with respect to the ground (V_monkey/ground), we use the formula:
\[ V_{monkey/ground} = V_{monkey/train} + V_{train} \]
Substituting the values:
\[ V_{monkey/ground} = -18 \text{ km/hr} + 54 \text{ km/hr} \]

### Step 5: Perform the calculation
\[ V_{monkey/ground} = 54 - 18 = 36 \text{ km/hr} \]

### Step 6: Determine the direction
Since the result is positive, the monkey is moving north at a speed of 36 km/hr.

### Step 7: Convert the speed to meters per second (if required)
To convert km/hr to m/s, we use the conversion factor \( \frac{5}{18} \):
\[ V_{monkey/ground} = 36 \text{ km/hr} \times \frac{5}{18} = 10 \text{ m/s} \]
Thus, the final velocity of the monkey as observed by a man standing on the ground is 10 m/s towards the north.

### Final Answer:
The velocity of the monkey as observed by a man standing on the ground is **10 m/s north**.

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