Final answer:
Using the kinematic equation for free fall, the ball dropped from a height of 8.1 meters will be traveling at approximately 12.6 m/s when it hits the ground.
Step-by-step explanation:
The student is asking about the final velocity of a ball that is dropped from a height of 8.1 meters onto the surface of the Earth. This is a classic physics problem that involves calculating the velocity of an object in free fall under the influence of Earth's gravity, disregarding air resistance.
To solve this, we use the following kinematic equation for free fall:
v = √(2gh)
where:
- v is the final velocity,
- g is the acceleration due to gravity (9.8 m/s2),
- h is the height from which the ball is dropped (8.1 m).
Plugging in the known values:
v = √(2 × 9.8 m/s2 × 8.1 m)
v = √(158.76 m2/s2)
v = 12.6 m/s
Therefore, the ball will be traveling at approximately 12.6 m/s when it hits the ground.