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A stone is dropped from the top of a tower 500 m high into a p... - Science
A stone is dropped from the top of a tower 500 m high into a pond of water at the base of the tower. When is the splash heard at the top? Given, g = 10 m s⁻² and speed of sound = 340 m s⁻¹.
Given:
Height (s) = 500\text{ m}g = 10\text{ m s}^{-2}
Speed of sound = 340\text{ m s}^{-1}
Initial velocity (u) = 0 (dropped)
Step 1: Time taken by the stone to reach the water (t_1):
Using equation: s = ut + \frac{1}{2} g t^2500 = (0 \times t_1) + \frac{1}{2} \times 10 \times t_1^2500 = 5 t_1^2t_1^2 = \frac{500}{5} = 100t_1 = \sqrt{100} = 10\text{ s}
Step 2: Time taken by sound to reach the top (t_2):t_2 = \frac{\text{Distance}}{\text{Speed of Sound}}t_2 = \frac{500}{340}t_2 \approx 1.47\text{ s}
Step 3: Total Time:
Total Time = t_1 + t_2
Total Time = 10 + 1.47 = 11.47\text{ s}
Answer:
The splash is heard at the top after 11.47\text{ s}.