the relationship between the final velocity of a dropped object, before striking the ground, and the starting height of the object?

Answer 1

The final velocity of a dropped object before striking the ground is directly related to the starting height of the object. This relationship is described by the equation for free fall:

v^2 = u^2 + 2as

Where:
v = final velocity of the object
u = initial velocity of the object (in this case, 0 m/s as the object is dropped)
a = acceleration due to gravity (9.81 m/s^2)
s = distance fallen (starting height of the object)

From this equation, we can see that the final velocity of the object before striking the ground is directly proportional to the square root of the starting height. In other words, the higher the object is dropped from, the greater the final velocity will be before it hits the ground.