Water drops fall from a tap on to the floor 5.0 m below at regular intervals of time. The first drop strikes the floor when the fifth drops beings to fall. The height at which the third drop will be from ground at the instant when the first drop strikes the ground is (take`=g=10 m^(-2)`)

Options

A. 1.25 m
B. 2.15 m
C. 2.75 m
D. 3.75 m

Explanation

To solve the problem, we need to determine the height of the third drop from the ground when the first drop strikes the ground. Here’s a step-by-step breakdown of the solution:

### Step 1: Determine the time taken for the first drop to hit the ground
The first drop falls from a height of 5 meters. We can use the equation of motion to find the time taken (t) for the first drop to reach the ground:

\[ h = ut + \frac{1}{2}gt^2 \]

Where:
- \( h = 5 \, \text{m} \)
- \( u = 0 \) (initial velocity)
- \( g = 10 \, \text{m/s}^2 \)

Substituting the values, we have:

\[ 5 = 0 \cdot t + \frac{1}{2} \cdot 10 \cdot t^2 \]

This simplifies to:

\[ 5 = 5t^2 \]

Dividing both sides by 5 gives:

\[ t^2 = 1 \implies t = 1 \, \text{s} \]

### Step 2: Determine the interval between successive drops
Since the first drop hits the ground when the fifth drop begins to fall, the time interval between each drop (let's denote it as \( \Delta t \)) can be calculated. The first drop takes 1 second to reach the ground, and there are 4 intervals between the 5 drops:

\[ 4\Delta t = 1 \implies \Delta t = \frac{1}{4} = 0.25 \, \text{s} \]

### Step 3: Calculate the time elapsed for the third drop
The third drop falls after 2 intervals of \( \Delta t \):

\[ \text{Time for third drop} = 2\Delta t = 2 \times 0.25 = 0.5 \, \text{s} \]

### Step 4: Calculate the distance fallen by the third drop
Now we need to find out how far the third drop has fallen in 0.5 seconds. We can use the same equation of motion:

\[ d = ut + \frac{1}{2}gt^2 \]

Where:
- \( u = 0 \)
- \( g = 10 \, \text{m/s}^2 \)
- \( t = 0.5 \, \text{s} \)

Substituting the values, we have:

\[ d = 0 \cdot 0.5 + \frac{1}{2} \cdot 10 \cdot (0.5)^2 \]

This simplifies to:

\[ d = 0 + \frac{1}{2} \cdot 10 \cdot 0.25 = 1.25 \, \text{m} \]

### Step 5: Determine the height of the third drop from the ground
The third drop has fallen 1.25 meters from the original height of 5 meters. Therefore, the height of the third drop from the ground is:

\[ \text{Height from ground} = 5 - 1.25 = 3.75 \, \text{m} \]

### Final Answer
The height at which the third drop will be from the ground at the instant when the first drop strikes the ground is **3.75 meters**.

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