A body of mass 2 kg is thrown vertically upwards with K.E of 245 J. The acceleration due to gravity is `9.8 ms^(-2)`. The K.E. Of the body will become half at the height of

Options

A. 25 m
B. `12.5 m`
C. `6.25 m`
D. `5 m`

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Determine the Initial Velocity
The initial kinetic energy (K.E) of the body is given as 245 J. The formula for kinetic energy is:

\[ K.E = \frac{1}{2} m u^2 \]

Where:
- \( m \) is the mass of the body (2 kg)
- \( u \) is the initial velocity

Substituting the values:

\[ 245 = \frac{1}{2} \times 2 \times u^2 \]

This simplifies to:

\[ 245 = 1 \times u^2 \]

So,

\[ u^2 = 245 \]

### Step 2: Calculate the Velocity When K.E is Half
We need to find the height at which the kinetic energy becomes half of the initial value. Half of 245 J is:

\[ K.E' = \frac{245}{2} = 122.5 \, J \]

Using the kinetic energy formula again:

\[ K.E' = \frac{1}{2} m v^2 \]

Substituting the values:

\[ 122.5 = \frac{1}{2} \times 2 \times v^2 \]

This simplifies to:

\[ 122.5 = v^2 \]

### Step 3: Apply the Conservation of Energy Principle
Using the conservation of energy, we can relate the initial kinetic energy and the potential energy at height \( h \):

\[ K.E_{\text{initial}} - K.E' = mgh \]

Where:
- \( g \) is the acceleration due to gravity (9.8 m/s²)

Substituting the values:

\[ 245 - 122.5 = 2 \times 9.8 \times h \]

This simplifies to:

\[ 122.5 = 19.6h \]

### Step 4: Solve for Height \( h \)
Now, we can solve for \( h \):

\[ h = \frac{122.5}{19.6} \]

Calculating this gives:

\[ h \approx 6.25 \, m \]

### Final Answer
The height at which the kinetic energy becomes half is approximately **6.25 meters**.

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