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:-

Explanation

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

### Step 1: Identify the velocities
- 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 directions
- Let's consider north as the positive direction.
- The velocity of the monkey relative to the train is negative since it is moving against the direction of the train.

### Step 3: Write the equations
- Let \( V_{train} = 54 \) km/hr (north).
- Let \( V_{monkey \, (relative \, to \, train)} = -18 \) km/hr (against the direction of the train).

### Step 4: Calculate the velocity of the monkey with respect to the ground
Using the formula for relative velocity:
\[ V_{monkey} = V_{monkey \, (relative \, to \, train)} + V_{train} \]
Substituting the values:
\[ V_{monkey} = -18 \, \text{km/hr} + 54 \, \text{km/hr} \]
\[ V_{monkey} = 36 \, \text{km/hr} \]

### Step 5: State the direction
Since the resulting velocity is positive, it indicates that the monkey is moving in the same direction as the train, which is north.

### Step 6: Convert to meters per second (if required)
To convert km/hr to m/s, we use the conversion factor \( \frac{5}{18} \):
\[ V_{monkey} = 36 \, \text{km/hr} \times \frac{5}{18} = 10 \, \text{m/s} \]

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

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