Also how to make good estimates, and how to work with units.
One example, the formula to get the speed of a thing after h meters of free fall must deliver an outcome of m/s. We also know the gravitational acceleration g is given in m/s^2. Then, height h in m must somehow be part of the formula. We can get rid of the squaresecond in the denominator by drawing the square root. But then we also need the height in meters. Also it is clear that both more height as well as a higher acceleration must lead to higher speed. Therefore, the speed must be proportional to sqrt(h x g). In fact it is v = 1/2 sqrt(h x g) but we can derive the important part only from knowing how to calculate with units.
Also how to make good estimates, and how to work with units.
One example, the formula to get the speed of a thing after h meters of free fall must deliver an outcome of m/s. We also know the gravitational acceleration g is given in m/s^2. Then, height h in m must somehow be part of the formula. We can get rid of the squaresecond in the denominator by drawing the square root. But then we also need the height in meters. Also it is clear that both more height as well as a higher acceleration must lead to higher speed. Therefore, the speed must be proportional to sqrt(h x g). In fact it is v = 1/2 sqrt(h x g) but we can derive the important part only from knowing how to calculate with units.