A boy weighing 40 kg climbs up a vertical height of 200 m. calculate the amount of work done by him. How much potential, energy does the pain?

Options

A. `2.84xx10^3 J`
B. `7.84xx10^4 J`
C. `8.74xx10^5 J`
D. `9.3xx10^6 J`

Answer

To solve the problem step by step, we will calculate the work done by the boy while climbing and the potential energy gained.

### Step 1: Identify the given values
- Mass of the boy (m) = 40 kg
- Height climbed (h) = 200 m
- Acceleration due to gravity (g) = 9.8 m/s² (approximately)

### Step 2: Use the formula for work done against gravity
The work done (W) against gravity when climbing to a height is given by the formula:
\[ W = m \cdot g \cdot h \]

### Step 3: Substitute the values into the formula
Now, substituting the known values into the formula:
\[ W = 40 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot 200 \, \text{m} \]

### Step 4: Perform the calculation
Calculating the above expression:
\[ W = 40 \cdot 9.8 \cdot 200 \]
\[ W = 40 \cdot 1960 \]
\[ W = 78400 \, \text{J} \]

### Step 5: Conclusion
The work done by the boy while climbing is 78,400 Joules. This work done is equal to the potential energy gained by the boy, since all the work done against gravity is converted into potential energy.

### Final Answer
- Amount of work done by the boy: **78,400 Joules**
- Potential energy gained: **78,400 Joules**

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