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bujorn
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Homework Statement
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.
Homework 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
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?
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