Final answer:
After falling for 1.55 seconds, the displacement of the ball dropped off a bridge is approximately 11.77 meters, which is the distance it has fallen.
Step-by-step explanation:
To determine how far a ball has fallen after being dropped off the side of a bridge for 1.55 seconds, you can use the formula for the distance covered during free fall under the influence of gravity. The formula for the displacement of an object in free fall is given by:
Δy = v_i × t + ½ × g × t^2
Where:
- Δy is the displacement (how far the ball has fallen),
- v_i is the initial velocity (which is 0 m/s since the ball is dropped),
- t is the time elapsed (1.55 s), and
- g is the acceleration due to gravity (which is approximately -9.80 m/s^2, the negative sign indicates that the acceleration is directed downwards towards the Earth's surface).
Inserting the values into the formula gives us:
Δy = 0 m/s × 1.55 s + ½ × (-9.80 m/s^2) × (1.55 s)^2
Δy = -0.5 × 9.80 m/s^2 × 2.4025 s^2
Δy = -11.7735 m
Since displacement is a vector quantity and the direction of the fall is downwards, the displacement is -11.7735 meters. However, when considering just the magnitude which is the actual distance fallen, we ignore the negative sign, and it is approximately 11.77 meters.
Therefore, after falling for 1.55 seconds, the ball has fallen approximately 11.77 meters.