Question

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

Answer 1

Answer:

A. The same amount

Explanation:

The acceleration at which objects free falls to the ground on Earth is constant and its value is always $9.81 m/s^2$, 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,

$F=mg$

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

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

$F=ma$

where a is the acceleration of the object.

Combining the two equations,

$ma=mg\\a=g$

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