Water drops fall from a tap onto the floor, 5 | vedclass

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Question

(C) Let the time interval between two consecutive drops be $t$. Since the first drop strikes the floor when the sixth drop begins to fall, the total t

Vedclass · Accepted Answer

$4.2$

Vedclass · Answer

(C) Let the time interval between two consecutive drops be $t$. Since the first drop strikes the floor when the sixth drop begins to fall, the total time taken by the first drop to reach the ground is $5t$. Given the height $h = 5 \ m$ and $g = 10 \ m/s^2$, the time taken is $t_{total} = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 	imes 5}{10}} = 1 \ s$. Thus, $5t = 1 \ s$, which implies $t = 0.2 \ s$. At the instant the first drop strikes the ground, the fourth drop has been falling for a time $t_4 = (5 - 4)t = 1 	imes 0.2 = 0.2 \ s$ is incorrect; let's re-evaluate: The first drop is at $t=0$ (start), $t=1$ (ground). The second drop is at $t=0.2$, the third at $t=0.4$, the fourth at $t=0.6$, the fifth at $t=0.8$, and the sixth at $t=1.0$. At $t=1.0 \ s$, the fourth drop has been falling for $(1.0 - 0.6) = 0.4 \ s$. Distance fallen by the fourth drop $h_4 = \frac{1}{2}gt_4^2 = \frac{1}{2} 	imes 10 	imes (0.4)^2 = 5 	imes 0.16 = 0.8 \ m$. Height from the ground $= 5 - 0.8 = 4.2 \ m$.

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