1. The problem statement, all variables and given/known data A man was standing on a cliff when he dropped a stone. One second later, he dropped another stone. How long before the distance between the two stone is 10 meters? (Show solutions with special attention to deriving the units.) Use g=10 m/s^2. 2. Relevant equations Let d_1 = depth of first stone Let d_2 = depth of second stone t_1 = time of first stone t_2 = time of second stone d_1 - d_2 = 10 d = (1/2)gt^2 t_1 = t t_2 = t-1 3. The attempt at a solution I usually solve problems like this but I really have not taken special attention how the units are derived. Since I know that the solving t would result in a unit of seconds, I neglect the units and continue to work on with the problem. d_1 - d_2 = 10 Substituting the formula for d in d_1 and d_2: (1/2)10t^2 - (1/2)10(t-1)^2 = 10 5t^2 - 5(t^2-2t+1) = 10 5t^2 - 5t^2 + 10t - 5 = 10 10t - 5 = 10 10t = 10 + 5 10t = 15 t = 15/10 or 1.5 sec I assumed that the equation is correct, thus t would result in unit of seconds. However, when I tried to solve the problem including the given units, I ended up like this: d_1 - d_2 = 10m (1/2)(10m/s^2)t^2 - (1/2)(10m/s^2)(t-1)^2 = 10m (5m/s^2)(t^2) - (5m/s^2)(t^2-2t+1) = 10 5mt^2/s^2 - 5mt^2/s^2 + 10mt/s^2 - 5m/s^2 = 10m 10mt/s^2 - 5m/s^2 = 10m (2t-1)5m/s^2=10m 2t - 1 = (10ms^2)/5m 2t - 1 = 2s^2 2t = 2s^2 + 1 t = (2s^2 + 1)/2 Where did I go wrong? Am I missing something?