Water drops fall from the roof of a building 20 m high at regular time intervals. If the first drop strikes the floor when the sixth drop begins to fall, the heights of the second and fourth drops from the ground at that instant are (g = 10 ms^–2)

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19.2m and 0.8m

12.8m and 3.2m

12.8m and 7.2m

7.2m and 16.8m

answer is D.

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Detailed Solution

$\begin{array}{l} h_{5} = \frac{1}{2} {gt}^{2} \\ h_{4} = \frac{1}{2} g (2 t)^{2} = 4 \cdot \frac{1}{2} {gt}^{2} \\ h_{3} = \frac{1}{2} g (3 t)^{2} = 9 \cdot \frac{1}{2} {gt}^{2} \\ h_{2} = \frac{1}{2} g (4 t)^{2} = 16 \cdot \frac{1}{2} {gt}^{2} \\ h_{1} = \frac{1}{2} g (5 t)^{2} = 25 \cdot \frac{1}{2} {gt}^{2} \\ h_{1} = 20 m; \frac{1}{2} {gt}^{2} = \frac{20}{25} \\ h_{2} = 16 \cdot \frac{1}{2} {gt}^{2} \Rightarrow h_{2} = \frac{16 \times 20}{25} = 12.8 \end{array}$
from ground (20 −12.8) = 7.2m
$h_{4} = 4 \cdot \frac{1}{2} {gt}^{2} \Rightarrow h_{4} = \frac{4 \times 20}{25} = 3.2 m$
from ground (20-3.2) = 16.8m