Discussion
If a freely falling body from the top of a tower takes 3 s and 5 s to cross the \(28^{th}\) floor and \(4^{th}\) floor respectively, then the height difference between these floors is (g = 10 ms−2)
Answer: A
The height difference is 80 m.
Falling from rest, the distance fallen in time \(t\) is \(\frac{1}{2}gt^{2}\):
\[ \begin{aligned} h_{3} &= \tfrac{1}{2}(10)(3)^{2} = 45\ \text{m} \\ h_{5} &= \tfrac{1}{2}(10)(5)^{2} = 125\ \text{m} \\ h_{5} - h_{3} &= 80\ \text{m} \end{aligned} \]
Using \(\frac{1}{2}g(5 - 3)^{2} = 20\) m treats the motion as if it restarted from rest, and the other options come from using \(gt\) or wrong times.
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