An elephant of length 4 m is at one corner of a rectangular cage of side `(16m xx 30m)` and faces towards the diagonally opposite corner. If the elephant starts moving towards the diagonally opposite corner it takes 15 seconds to reach this corner. Find the speed of the elephant.

Options

A. 1m/sec
B. 2m/sec
C. 1.87 m/sec
D. 1.5 m/sec

Answer

To find the speed of the elephant, we can follow these steps:

### Step 1: Determine the dimensions of the cage
The rectangular cage has dimensions of 16 m and 30 m.

### Step 2: Calculate the length of the diagonal of the rectangle
To find the diagonal (AC) of the rectangle, we can use the Pythagorean theorem:
\[ AC = \sqrt{(length)^2 + (width)^2} = \sqrt{(30)^2 + (16)^2} \]
Calculating this gives:
\[ AC = \sqrt{900 + 256} = \sqrt{1156} = 34 \text{ m} \]

### Step 3: Adjust for the length of the elephant
Since the elephant has a length of 4 m, it will reach the diagonally opposite corner 4 m before it actually reaches the corner. Therefore, the distance traveled by the elephant is:
\[ \text{Distance traveled} = AC - \text{length of the elephant} = 34 \text{ m} - 4 \text{ m} = 30 \text{ m} \]

### Step 4: Calculate the time taken to travel this distance
The time taken for the elephant to reach the corner is given as 15 seconds.

### Step 5: Calculate the speed of the elephant
Speed is calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{30 \text{ m}}{15 \text{ s}} = 2 \text{ m/s} \]

### Final Answer
The speed of the elephant is **2 m/s**.

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