Falling Object with Air Resistance?

📌 CONCEPT: The concept of a falling object with air resistance can be modeled using the equation of motion under gravity with an additional term to account for the effect of air resistance, which is proportional to the velocity of the object.

📐 RULE / FORMULA: The equation of motion can be represented by the function s(t) = ut + Λgt^2 - (kv)t, where s(t) is the distance fallen at time t, u is the initial velocity (0 in this case), t is the time, g is the acceleration due to gravity, Λ is a constant representing the effect of air resistance, and k is a constant related to the air resistance.

💡 WORKED EXAMPLE: To find the distance fallen by the stone in 3 seconds, we can use the given function s(t) = 100 - (2/2)t^2, where the initial velocity u = 0, the constant k = 2 m/s, and the acceleration due to gravity g = 9.8 m/s^2. Substituting t = 3 into the equation, we get s(3) = 100 - (2/2)(3)^2 = 100 - 9 = 91 m.

⚠️ COMMON MISTAKE: Students may forget to include the effect of air resistance in the equation of motion, or use an incorrect value for the constant k related to air resistance.