From the top of a 490 m high cliff, a boy throws a stone horizontally with a initial speed of ` 15 ms^(-1)`. What is the time taken by the stone to reach the ground.

Options

A. 5 s
B. 10 s
C. 12 s
D. 15 s

Explanation

To solve the problem of finding the time taken by the stone to reach the ground after being thrown horizontally from a height of 490 m, we can follow these steps:

### Step 1: Identify the given data
- Height of the cliff (h) = 490 m
- Initial horizontal speed (u) = 15 m/s (not needed for time calculation)
- Acceleration due to gravity (g) = 9.8 m/s²

### Step 2: Use the formula for time of flight
The time taken to fall from a height h under gravity can be calculated using the formula:
\[ t = \sqrt{\frac{2h}{g}} \]

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ t = \sqrt{\frac{2 \times 490}{9.8}} \]

### Step 4: Simplify the expression
Calculating the numerator:
\[ 2 \times 490 = 980 \]
Now substituting back into the equation:
\[ t = \sqrt{\frac{980}{9.8}} \]

### Step 5: Perform the division
Calculating the division:
\[ \frac{980}{9.8} = 100 \]

### Step 6: Calculate the square root
Now, taking the square root:
\[ t = \sqrt{100} = 10 \text{ seconds} \]

### Conclusion
The time taken by the stone to reach the ground is **10 seconds**.

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