In a shotput event an athlete throws the shotput of mass `10 kg` with an initial speed of `1 ms^(-1)` at `45^@` from a height `1.5 m` above ground. Assuming air resistance to be negligible and acceleration due to gravity to be `10 ms^(-2)`, the kinetic energy of the shotput when it just reaches the ground will be

Options

A. 2.5 J
B. 5 J
C. 52.5 J
D. 155 J

Explanation

To find the kinetic energy of the shotput when it just reaches the ground, we can use the principle of conservation of mechanical energy. The total mechanical energy (sum of potential energy and kinetic energy) at the initial height will be equal to the total mechanical energy when the shotput reaches the ground.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the shotput, \( m = 10 \, \text{kg} \)
- Initial speed, \( v = 1 \, \text{m/s} \)
- Angle of throw, \( \theta = 45^\circ \) (not needed for this calculation)
- Initial height, \( h = 1.5 \, \text{m} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

2. **Calculate Initial Potential Energy (PE_initial):**
\[ PE_{\text{initial}} = mgh = 10 \, \text{kg} \times 10 \, \text{m/s}^2 \times 1.5 \, \text{m} = 150 \, \text{J} \]

3. **Calculate Initial Kinetic Energy (KE_initial):**
\[ KE_{\text{initial}} = \frac{1}{2} mv^2 = \frac{1}{2} \times 10 \, \text{kg} \times (1 \, \text{m/s})^2 = \frac{1}{2} \times 10 \times 1 = 5 \, \text{J} \]

4. **Calculate Total Initial Mechanical Energy:**
\[ E_{\text{initial}} = PE_{\text{initial}} + KE_{\text{initial}} = 150 \, \text{J} + 5 \, \text{J} = 155 \, \text{J} \]

5. **At the Ground Level:**
- When the shotput reaches the ground, the height is \( h = 0 \), so the potential energy at this point is:
\[ PE_{\text{final}} = 0 \, \text{J} \]
- Therefore, all the initial mechanical energy will convert to kinetic energy at the ground level:
\[ KE_{\text{final}} = E_{\text{initial}} = 155 \, \text{J} \]

6. **Final Answer:**
The kinetic energy of the shotput when it just reaches the ground is \( KE_{\text{final}} = 155 \, \text{J} \).