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A stone dropped from the top of a tower of height 300 m high splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is 340 ms-1 ? (g = 9.8 ms-2 )

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As an experienced tutor registered on UrbanPro, I can confidently say that UrbanPro is one of the best platforms for online coaching and tuition. Now, let's tackle your physics problem. We have a stone dropped from a tower, and we need to find out when the splash is heard at the top of the tower. We'll...
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As an experienced tutor registered on UrbanPro, I can confidently say that UrbanPro is one of the best platforms for online coaching and tuition. Now, let's tackle your physics problem.

We have a stone dropped from a tower, and we need to find out when the splash is heard at the top of the tower. We'll first determine the time it takes for the stone to fall to the pond and then the time it takes for the sound of the splash to travel back up to the top of the tower.

  1. Time taken for the stone to fall: Using the equation of motion: s=ut+12at2s=ut+21at2 where:
  • ss is the height of the tower (300 m),
  • uu is the initial velocity (0 m/s since it's dropped),
  • aa is the acceleration due to gravity (-9.8 m/s²),
  • tt is the time taken.

300=0×t+12×(−9.8)×t2300=0×t+21×(−9.8)×t2 300=−4.9t2300=−4.9t2 t2=3004.9t2=4.9300 t2≈61.22t2≈61.22 t≈61.22t≈61.22

t≈7.82t≈7.82 seconds (approximately)

So, it takes roughly 7.82 seconds for the stone to fall to the pond.

  1. Time taken for the sound of the splash to travel up: We can use the formula: v=stv=ts where:
  • vv is the velocity of sound (340 m/s),
  • ss is the distance sound travels (300 m, the height of the tower),
  • tt is the time taken.

340=300t340=t300 t=300340t=340300 t≈0.88t≈0.88 seconds (approximately)

So, it takes roughly 0.88 seconds for the sound of the splash to travel up to the top of the tower.

Now, we add the time taken for the stone to fall to the pond and the time taken for the sound of the splash to travel up: Total time=7.82+0.88Total time=7.82+0.88 Total time≈8.7Total time≈8.7 seconds (approximately)

Therefore, the splash is heard at the top of the tower after approximately 8.7 seconds.

 
 
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