A ball thrown vertically upwards with an initial velocity of `1.4 m//s.` The total displcement of the ball is

Options

A. `22.4cm`
B. zero
C. `44.8m`
D. `33.6m`

Answer

To solve the problem of finding the total displacement of a ball thrown vertically upwards with an initial velocity of 1.4 m/s, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Displacement**: Displacement is defined as the change in position of an object. It is a vector quantity that has both magnitude and direction.

2. **Initial Conditions**: The ball is thrown vertically upwards with an initial velocity (u) of 1.4 m/s.

3. **Motion of the Ball**: As the ball moves upwards, it will eventually reach a maximum height where its velocity will become zero due to the acceleration of gravity acting downwards (g = 9.81 m/s²).

4. **Maximum Height Calculation**:
- To find the maximum height (h) reached by the ball, we can use the kinematic equation:
\[ v^2 = u^2 + 2a s \]
where:
- \( v = 0 \) m/s (final velocity at the maximum height),
- \( u = 1.4 \) m/s (initial velocity),
- \( a = -g = -9.81 \) m/s² (acceleration due to gravity),
- \( s = h \) (displacement or height reached).

Rearranging the equation gives:
\[ 0 = (1.4)^2 + 2(-9.81)h \]
\[ 0 = 1.96 - 19.62h \]
\[ 19.62h = 1.96 \]
\[ h = \frac{1.96}{19.62} \approx 0.1 \text{ m} \]

5. **Total Displacement**:
- After reaching the maximum height, the ball will fall back down to the original position (the point from where it was thrown).
- Since displacement is the difference between the final position and the initial position, and both positions are the same (the ball returns to the original point), the total displacement is:
\[ \text{Total Displacement} = \text{Final Position} - \text{Initial Position} = 0 \text{ m} \]

### Conclusion:
The total displacement of the ball is **0 meters**.