A woman throws and object of mass `500g` with a speed of `25ms^(-1)`. If the object hits a wall and rebounds with half the original speed, what is the change in momentum of the object?

Options

A. `-18.75 N-S`
B. `18.75 N-S`
C. `-20.75 N-S`
D. `20.75 N-S`

Explanation

To solve the problem, we need to calculate the change in momentum of the object when it is thrown, hits the wall, and rebounds. Here are the steps to find the solution:

### Step 1: Convert mass to kilograms
The mass of the object is given as 500 grams. We need to convert this to kilograms because the standard unit of mass in physics is kilograms (kg).

\[ \text{Mass} (m) = 500 \, \text{g} = \frac{500}{1000} \, \text{kg} = 0.5 \, \text{kg} \]

### Step 2: Calculate the initial momentum
The initial momentum (p_initial) of the object can be calculated using the formula:

\[ p_{\text{initial}} = m \times v_{\text{initial}} \]

Where:
- \( m = 0.5 \, \text{kg} \)
- \( v_{\text{initial}} = 25 \, \text{m/s} \)

Substituting the values:

\[ p_{\text{initial}} = 0.5 \, \text{kg} \times 25 \, \text{m/s} = 12.5 \, \text{kg m/s} \]

### Step 3: Calculate the final velocity
The object rebounds with half the original speed. Therefore, the final speed (v_final) after rebounding is:

\[ v_{\text{final}} = \frac{25}{2} \, \text{m/s} = 12.5 \, \text{m/s} \]

Since the object is moving in the opposite direction after rebounding, we will consider this speed as negative:

\[ v_{\text{final}} = -12.5 \, \text{m/s} \]

### Step 4: Calculate the final momentum
The final momentum (p_final) of the object can be calculated using the same formula:

\[ p_{\text{final}} = m \times v_{\text{final}} \]

Substituting the values:

\[ p_{\text{final}} = 0.5 \, \text{kg} \times (-12.5 \, \text{m/s}) = -6.25 \, \text{kg m/s} \]

### Step 5: Calculate the change in momentum
The change in momentum (Δp) is given by the formula:

\[ \Delta p = p_{\text{final}} - p_{\text{initial}} \]

Substituting the values we calculated:

\[ \Delta p = -6.25 \, \text{kg m/s} - 12.5 \, \text{kg m/s} = -18.75 \, \text{kg m/s} \]

### Final Answer
The change in momentum of the object is:

\[ \Delta p = -18.75 \, \text{kg m/s} \]