Understanding Distance and Displacement for Ball Motion

The question describes a scenario where a ball is thrown vertically upwards with a certain velocity, reaches a maximum height, and then returns to the thrower. We need to determine the total distance covered and the total displacement.

Defining Distance and Displacement

Let's first clarify the key terms:

• Distance: This is the total length of the path traveled by an object. It is a scalar quantity, meaning it only has magnitude and no direction.
• Displacement: This is the change in position of an object. It is the shortest straight-line distance between the initial and final points, and it is a vector quantity, meaning it has both magnitude and direction.

Calculating Total Distance

The ball is thrown upwards and reaches a maximum height of 50 meters from the thrower. It then falls back down to the thrower. The path taken is:

1. Upwards from the thrower to the maximum height (50 m).
2. Downwards from the maximum height back to the thrower (50 m).

The total distance covered is the sum of the distance traveled upwards and the distance traveled downwards.

Total Distance = Distance (up) + Distance (down)

Total Distance = 50 m + 50 m = 100 m

So, the total distance covered by the ball is 100 meters.

Calculating Total Displacement

Displacement is the change in position. We need to compare the initial position with the final position.

• Initial position: The ball starts at the thrower's hand.
• Final position: The ball returns to the thrower's hand.

Since the ball starts and ends at the same location, its initial position is the same as its final position.

Displacement is calculated as:

Displacement = Final Position - Initial Position

In this case, since the initial and final positions are identical, the change in position is zero.

Total Displacement = 0 meters

Therefore, the total displacement of the ball is zero.

Conclusion on Ball Motion

For the described motion where the ball goes up 50 m and comes back to the thrower, the total distance is 100 m, and the total displacement is 0 m.

Reviewing the options:

• Total distance covered by it is 50 m (Incorrect - distance is 100 m)
• Total displacement covered by it is 100 m (Incorrect - displacement is 0 m)
• Total displacement is zero (Correct)
• Total distance covered by it is 120 m (Incorrect - distance is 100 m)

Based on our calculations, the correct statement is that the total displacement is zero.