A golf ball of mass m is hit by a golf club so that the ball leaves the tee with speed v. The club is in contact with the ball for time T. The magnitude of the average force on the club on the ball during the time T is :

Options

A. `mv T`
B. `mv//T`
C. `(1//2) mv^2 T`
D. `mv^2 (2T)`

Explanation

To solve the problem, we need to determine the average force exerted by the golf club on the golf ball during the time of contact \( T \). We'll use the concept of momentum and the definition of average force.

### Step-by-Step Solution:

1. **Identify Initial and Final Conditions**:
- The mass of the golf ball is \( m \).
- The initial velocity of the ball \( u = 0 \) (the ball is at rest before being hit).
- The final velocity of the ball after being hit is \( v \).

2. **Calculate the Change in Momentum**:
- The momentum of an object is given by the product of its mass and velocity.
- The initial momentum \( p_i \) of the ball is:
\[ p_i = m \cdot u = m \cdot 0 = 0 \]
- The final momentum \( p_f \) of the ball is:
\[ p_f = m \cdot v \]
- The change in momentum \( \Delta p \) is:
\[ \Delta p = p_f - p_i = mv - 0 = mv \]

3. **Determine the Average Force**:
- The average force \( F_{\text{avg}} \) is defined as the change in momentum divided by the time interval during which the change occurs:
\[ F_{\text{avg}} = \frac{\Delta p}{\Delta t} \]
- Here, \( \Delta t = T \) (the time the club is in contact with the ball).
- Substituting the change in momentum:
\[ F_{\text{avg}} = \frac{mv}{T} \]

4. **Final Result**:
- Therefore, the magnitude of the average force exerted by the club on the ball is:
\[ F_{\text{avg}} = \frac{mv}{T} \]