Fig. shows an estimated force-time graph for a base ball struck by a bat. From this curve, determine
(i) impulse delivered to the ball
(ii) force exerted on the ball
(iii) the maximum force on the ball.

Answer

To solve the problem step by step, we will analyze the force-time graph for the baseball struck by a bat.

### Step 1: Determine the Impulse Delivered to the Ball
Impulse is defined as the area under the force-time graph. In this case, we have a triangular area on the graph.

1. **Identify the base and height of the triangle:**
- The base of the triangle is the time interval from 1 to 2.5 seconds, which is \(2.5 - 1 = 1.5\) seconds.
- The height of the triangle, which represents the maximum force, is 18000 N.

2. **Calculate the area of the triangle (impulse):**
\[ \text{Impulse} = \text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} \]
\[ \text{Impulse} = \frac{1}{2} \times 1.5 \, \text{s} \times 18000 \, \text{N} \]
\[ \text{Impulse} = \frac{1}{2} \times 1.5 \times 18000 = 13500 \, \text{N·s} \]

### Step 2: Determine the Average Force Exerted on the Ball
The average force exerted on the ball can be calculated using the impulse and the time interval over which the impulse is delivered.

1. **Use the formula for average force:**
\[ \text{Average Force} = \frac{\text{Impulse}}{\text{Time interval}} \]
\[ \text{Average Force} = \frac{13500 \, \text{N·s}}{1.5 \, \text{s}} = 9000 \, \text{N} \]

### Step 3: Determine the Maximum Force on the Ball
The maximum force exerted on the ball can be directly read from the force-time graph.

1. **Identify the maximum force:**
- From the graph, the maximum force is at the peak of the triangle, which is 18000 N.

### Summary of Results
- **Impulse Delivered to the Ball:** \(13500 \, \text{N·s}\)
- **Average Force Exerted on the Ball:** \(9000 \, \text{N}\)
- **Maximum Force on the Ball:** \(18000 \, \text{N}\)