Question

The water drops fall at regular intervals from a tap $5m$ above the ground. Let us assume that the third drop is falling from the tap at the exact moment the first touches the ground. What will be the distance above the ground to the second drop at that moment?
$\begin{aligned} & A.1.25m \\\ & B.2.50m \\\ & C.3.75m \\\ & D.4.00m \\\ \end{aligned}$

Answer 1

Find the time taken for the fall of the first drop from the tap using the second equation of motion. Then using this find the time interval between the first drop and the second drop. Using the second equation of motion find out the distance travelled by the drop to touch the ground from its initial position. The difference between the height of the tap and the initial height of the second drop will be the height from the ground. This all will help you in solving this question.

Complete step by step answer:
The height of the tap is given as,
$h=5m$
And the acceleration due to gravity is given as,
$g=10m{{s}^{-2}}$
For the first drop, we can apply the second equation of motion which can be written as,
$s=ut+\dfrac{1}{2}a{{t}^{2}}$
Initially the velocity will be zero. That is,
$u=0$
And
$a=g$
Substituting the values in it will give,

& 5=0\times t+\dfrac{1}{2}\times 10\times {{t}^{2}} \\\ & \Rightarrow 5=5{{t}^{2}} \\\ & \Rightarrow {{t}^{2}}=1 \\\ & \therefore t=1 \\\ \end{aligned}$$ This means that the third drop will be falling down after one second of the first drop. Or we can say that each drop leaves after every $$0.5s$$. Now let us find out the distance travelled by the drop to touch the ground from its initial position. That is we can write that, $$s=\dfrac{1}{2}\times 10\times {{\left( 0.5 \right)}^{2}}=1.25m$$ Hence the distance of the second drop above the ground can be written as, $$x=h-s$$ Substituting the values in it will give, $$x=5-1.25=3.75m$$  **Therefore the answer has been obtained as option C.** **Note:** Displacement is the shortest distance of the path which can be taken for travel. It can be measured as the perpendicular distance from the initial position to the final position. The distance is a scalar quantity, while displacement is a vector.