First slide

Position Path Length (Distance) And Displacement

Question

The water drops fall at regular interval from a tap 5 m above the ground. The third drop is leaving the tap at instant the first drop touches the ground. How far above the ground is the second drop at that instant ?

Easy

A

1.25 m
B

2.50 m
C

3.75 m
D

4.00 m

Solution

See figure. Let t be the time interval between any two drops.
For third drop $5 = \frac{1}{2} g (2 t)^{2} or {gt}^{2} = 5 / 2$
For second drop $x = \frac{1}{2} {gt}^{2}$
or $x = \frac{1}{2} \times \frac{5}{2} = \frac{5}{4} = 1 \cdot 25 m$
Therefore h = 5 - x = 5 - 1.25 = 3 . 75 m

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