A stationary ball weighing 0.25 kg acquires a speed of 10m/s when hit by a hockey stick. The impulse imparted to the ball is

Options

A. 2.5 Ns
B. 2.0 Ns
C. 1.5 Ns
D. 0.5 Ns

Explanation

To find the impulse imparted to the ball, we can follow these steps:

### Step 1: Understand the concept of impulse
Impulse is defined as the change in momentum of an object when a force is applied over a period of time. Mathematically, impulse (J) can be expressed as:
\[ J = \Delta P \]
where \( \Delta P \) is the change in momentum.

### Step 2: Determine the initial and final momentum
1. **Initial Momentum (P_initial)**: Since the ball is stationary before being hit, its initial velocity (u) is 0 m/s. The mass (m) of the ball is given as 0.25 kg.
\[ P_{\text{initial}} = m \times u = 0.25 \, \text{kg} \times 0 \, \text{m/s} = 0 \, \text{kg m/s} \]

2. **Final Momentum (P_final)**: After being hit, the ball acquires a speed (v) of 10 m/s.
\[ P_{\text{final}} = m \times v = 0.25 \, \text{kg} \times 10 \, \text{m/s} = 2.5 \, \text{kg m/s} \]

### Step 3: Calculate the change in momentum
The change in momentum (\( \Delta P \)) can be calculated as:
\[ \Delta P = P_{\text{final}} - P_{\text{initial}} = 2.5 \, \text{kg m/s} - 0 \, \text{kg m/s} = 2.5 \, \text{kg m/s} \]

### Step 4: Relate change in momentum to impulse
Since impulse is equal to the change in momentum:
\[ J = \Delta P = 2.5 \, \text{kg m/s} \]

### Step 5: State the final answer
The impulse imparted to the ball is:
\[ J = 2.5 \, \text{Ns} \]

### Conclusion
Thus, the impulse imparted to the ball is **2.5 Ns**.

---