Exploring Physics: Finding the Speed of a Falling Ball

How fast is a ball moving when it hits the sidewalk after being dropped from a height of 3.5 m?

Answer:

Final answer: To find the speed at which a ball hits the sidewalk when dropped from 3.5 m, we use the kinematic equation v^2 = u^2 + 2gh, with g as 9.8 m/s^2 and h as 3.5 m, resulting in a final velocity of approximately 8.28 m/s.

Explanation:

The subject of the question is Physics, and the grade level is high school. The student asks how fast a ball is moving when it hits the sidewalk if dropped from a window 3.5 meters above the ground. To solve this problem, we can use the kinematic equation for an object in free fall under Earth's gravity. The equation is v^2 = u^2 + 2gh, where v is the final velocity, u is the initial velocity (which is 0 in this case as the ball is dropped), g is the acceleration due to gravity (approximately 9.8 m/s2), and h is the height (3.5 m in this case).

By plugging the known values into the kinematic equation, we can solve for the final velocity:

v^2 = 0^2 + 2(9.8 m/s^2)(3.5 m)

v^2 = 2(9.8)(3.5)

v^2 = 68.6 m^2/s^2

v = √(68.6 m^2/s^2)

v ≈ 8.28 m/s

Therefore, the ball would be moving at approximately 8.28 meters per second when it hits the sidewalk.