Drop a rock from a 5-m height and it accelerates at 9.81 m/s^2 and strikes the ground 1s later. drop the sane rock from a height of 2.5m and it’s acceleration of fall is about

a. the same amount
b. greater than the second height
c. less than the second height
d. acceleration

A. The same amount

Explanation:

The acceleration at which objects free falls to the ground on Earth is constant and its value is always , regardless of their mass (in this problem we neglect air resistance).

So, it doesn't matter if the two rocks are different or they are launched from different heights: their acceleration will be exactly the same.

This can be proved this way: first of all, the force of gravity exerted on every object is equal to the weight of the object,

where m is the mass of the object and g the acceleration of gravity.

However, we also know for Newton's second law that

where a is the acceleration of the object.

Combining the two equations,

So, the acceleration of an object in free fall is exactly the acceleration of gravity.

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