A hockey ball of mass `200 g` travelling at `10 m//s` is struck by a hockey stick so as to return it along its original path with a velocity of `5 m//s`. Calculate the change in momentum of the hockey ball by the force applied by the hockey stick.

Explanation

To calculate the change in momentum of the hockey ball when it is struck by the hockey stick, we can follow these steps:

### Step 1: Convert the mass of the hockey ball into kilograms
The mass of the hockey ball is given as 200 grams. To convert this into kilograms, we use the conversion factor \(1 \text{ kg} = 1000 \text{ g}\).

\[ \text{Mass (m)} = \frac{200 \text{ g}}{1000} = 0.2 \text{ kg} \]

### Step 2: Calculate the initial momentum
The initial momentum (\(P_i\)) of the hockey ball can be calculated using the formula:

\[ P_i = m \cdot v_i \]

Where:
- \(m = 0.2 \text{ kg}\) (mass of the ball)
- \(v_i = 10 \text{ m/s}\) (initial velocity)

Substituting the values:

\[ P_i = 0.2 \text{ kg} \cdot 10 \text{ m/s} = 2 \text{ kg m/s} \]

### Step 3: Calculate the final momentum
The final momentum (\(P_f\)) of the hockey ball after being struck is calculated similarly. The final velocity (\(v_f\)) is given as 5 m/s, but since it is moving in the opposite direction, we will consider it as negative:

\[ P_f = m \cdot v_f \]

Where:
- \(v_f = -5 \text{ m/s}\) (final velocity)

Substituting the values:

\[ P_f = 0.2 \text{ kg} \cdot (-5 \text{ m/s}) = -1 \text{ kg m/s} \]

### Step 4: Calculate the change in momentum
The change in momentum (\(\Delta P\)) is given by the formula:

\[ \Delta P = P_f - P_i \]

Substituting the values we calculated:

\[ \Delta P = -1 \text{ kg m/s} - 2 \text{ kg m/s} = -3 \text{ kg m/s} \]

### Conclusion
The change in momentum of the hockey ball is \(-3 \text{ kg m/s}\).

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