2.3 The Acceleration Due to Gravity
When a model ignoring air resistance is used, all objects falling freely under gravity fall with the same constant acceleration, g m s−2 . This varies over the surface of the earth (Gravity of Earth - Wikipedia).
In our lessons it is assumed that all the situations occur in a place where it is 10 m s−2 . The value 9.8 m s−2 is also used. Most answers are given correct to three significant figures so that you can check your working.
Question 2.3.1:
A coin is dropped from rest at the top of a building of height 12 m and travels in a straight line with constant acceleration 10 m s−2. Find the time it takes to reach the ground and the speed of impact.
Solution 2.3.1:
Figure 2.9
Suppose the time taken to reach the ground is t seconds. Using S.I. units, u = 0, a = 10 and s = 12 when the coin hits the ground, so you need to use a formula involving u, a, s and t.
To find the velocity, v, a formula involving s, u, a and v is required.
The coin takes 1.55 s to hit the ground and has speed 15.5 m s−1 on impact.
Summary:
The formulae for motion with constant acceleration are:
