A stone is dropped into a lake by a person from a 500 m high tower. He would hear the sound of after approximately. (a) 10 s (b) 11.5 s (c) 14 s (d) 21 s

To determine how long it takes for a person to hear the sound of a stone dropped from a 500 m high tower, we need to consider two main components: the time it takes for the stone to fall and the time it takes for the sound to travel back up to the person. Let's break this down step by step.

Calculating the Fall Time of the Stone

The stone is dropped from a height of 500 meters. We can use the physics formula for free fall, which is:

h = (1/2)gt²

Where:

• h = height (500 m)
• g = acceleration due to gravity (approximately 9.81 m/s²)
• t = time in seconds

Rearranging the formula to solve for time (t), we get:

t = √(2h/g)

Substituting the values:

t = √(2 * 500 m / 9.81 m/s²)

Calculating this gives:

t ≈ √(101.83) ≈ 10.09 seconds

Calculating the Sound Travel Time

Next, we need to calculate how long it takes for the sound to travel back up to the person. The speed of sound in air is approximately 343 m/s. The distance the sound needs to travel is the same height of the tower, which is 500 m. We can use the formula:

time = distance / speed

Substituting the values:

time = 500 m / 343 m/s

Calculating this gives:

time ≈ 1.46 seconds

Combining Both Times

Now, we add the time it took for the stone to fall and the time it took for the sound to travel back up:

Total time = fall time + sound travel time

Total time ≈ 10.09 seconds + 1.46 seconds ≈ 11.55 seconds

Final Answer

Rounding this to a reasonable approximation, the total time it takes for the person to hear the sound after dropping the stone is approximately 11.5 seconds. Therefore, the correct answer is (b) 11.5 s.