2. To estimate the depth of an abandoned well, a piece of stone is dropped from rest into it and a stopwatch is started. The stopwatch is stopped as soon as the stone hits the water surface. Let d be the distance between the well's entrance and the water surface and T be the reading on the stopwatch. (a) Express d in terms of T and g. Check that the expression has equal units on both sides of the equation. [Note: Neglect air resistance.] (b) The reading on the stopwatch is 5.5 s, with an uncertainty AT = 0.5 s. Calculate the measured d and its uncertainty Ad. [Hint: For f = aA¹, its uncertainty is given by |4f| labAb-¹AA).] ≈ (c) You drop another stone and obtain 5.5 s, with the same uncertainty. The average of the two measurements is taken as dnew. What is the new uncertainty Adnew? [Hint: For f = aA + bB, its uncertainty is given by |4f|≈ √a²4A² + b²4B².]

2. To estimate the depth of an abandoned well, a piece of stone is dropped from rest into it and a stopwatch is started. The stopwatch is stopped as soon as the stone hits the water surface. Let d be the distance between the well's entrance and the water surface and T be the reading on the stopwatch. (a) Express d in terms of T and g. Check that the expression has equal units on both sides of the equation. [Note: Neglect air resistance.] (b) The reading on the stopwatch is 5.5 s, with an uncertainty AT = 0.5 s. Calculate the measured d and its uncertainty Ad. [Hint: For f = aA¹, its uncertainty is given by |4f| labAb-¹AA).] ≈ (c) You drop another stone and obtain 5.5 s, with the same uncertainty. The average of the two measurements is taken as dnew. What is the new uncertainty Adnew? [Hint: For f = aA + bB, its uncertainty is given by |4f|≈ √a²4A² + b²4B².]