1. A small stone is dropped from a height of 25 meters above the ground. i) Find the time taken for the stone to reach the ground ii) Find the speed of the stone as it reaches the ground

i) Let’s first write down, as we always should, what we know and what we are searching for. We know height is 25 meters and we are searching for time, so: ℎ = 25 �� �� =? This is a case of free fall of course, and rather than searching for the appropriate free fall equation, let’s look how we could derive it from a more general kinematics equation. Let’s try and remember most basic horizontal linear motion. If we have linear accelerated motion, what would be our equation for distance traveled? �� = ���� + 1 2 ���� 2 This is for horizontal linear motion, but in our case how much different things really are? The stone has a straight down, therefore linear trajectory, and it is accelerated due to gravity so we just adjust the equation. Our distance traveled is now h instead of s, and acceleration is g instead of a. ℎ = ���� + 1 2 ���� 2 And so we have the equation for distance, or better say height, travelled during free fall. There is no mention of initial velocity, therefore �� = 0 and so the equation is reduced to ℎ = 1 2 ���� 2 And we must solve it for t. So let’s put unknown variable on one side and everything else on the right. We are going to divide both sides of the equation with g and multiply it with two and this gives us: 2ℎ �� = �� 2 �� 2 = 2ℎ �� We’ve just rotated the equation, since as a rule we want unknown variable to be on the left. Now we just do the square root of both sides of the equation in order to just have value of t: �� = √ 2ℎ �� And here we have our final equation for the time of free fall, without the initial velocity, from a certain height h. Only now when we have the final expression in equation form should we input our values and calculate the final answer. I realize numbers must seem easier to operate with rather than variables, but this is only at first, as our knowledge of math and physics expands, so will the equations, and numbers will only increase the chance of confusion and accidental mistake. So let’s now input values along with the appropriate units of course and thus finish our problem. �� = √ 2 ∗ 25 �� 9.81 ��/�� 2 �� = 2.3 �� Our calculator gives us value �� = 2.257618205 �� but we can round it up to two significant figures, as we did.