a ball bounces three times before it is caught. it initially falls 5 m, then rises back up to 4m, then falls 4m, rises back up to 3m, then falls 1.5m where it is caught. what is the balls displacement from its original position 5m above the ground?
it starts at h = 5
it ends at h = 1.5
it fell 3.5 meters
To find the ball's displacement from its original position, you need to calculate the sum of all the individual displacements. Displacement is a vector quantity, so we need to account for both the magnitude (distance) and direction.
Let's break down the ball's motion:
1. It initially falls 5m downwards, so the displacement is -5m (negative sign indicating downward direction).
2. It rises back up to 4m, so the displacement is +4m (positive sign indicating upward direction).
3. It falls 4m downwards, so the displacement is -4m.
4. It rises back up to 3m, so the displacement is +3m.
5. Finally, it falls 1.5m downwards and is caught, so the displacement is -1.5m.
To calculate the total displacement, sum up all the individual displacements:
Displacement = -5m + 4m - 4m + 3m - 1.5m
Simplifying, we get:
Displacement = -3.5m
Therefore, the ball's displacement from its original position, 5m above the ground, is -3.5m. The negative sign indicates that the ball has moved downwards from its initial position.