Question

A stone is dropped from a 80m tall building into a pond. Find the time when the sound will be heard if speed of sound is 330m/s.​

Answer 1

Given

• Height of the Building = 80 m
• Gravitational Acceleration = 10 m/s²
• Speed of sound = 300 m/s

To Find

• Time when the sound would be heard

Solution

● s = ut + ½at²

● Speed = Distance/Time

● Here we shall use tye second equation of motion to find the time taken by the ball to hit the pond. Then use the formula of speed to find the time taken by the sound to travel from the pond to the top of the building. Their dum would be our time taken and hence our answer!!

✭ Time taken by the ball to hit the pond :

→ s = ut + ½at²

→ 80 = 0 × t + ½ × 10 × t²

→ 80 = 5 × t²

→ 80/5 = t²

→ 16 = t²

→ t = √16

→ t = 4 sec

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✭ Time taken by the sound to reach back :

→ Speed = Distance/Time

→ 330 = 80/Time

→ Time = 80/330

→ Time = 0.24 sec

━━━━━━━━━━━━━━━━━━━━━━

• Total Time = Time for the stone to hit the pond + Time for the sound to reach back
• Total Time = 4 + 0.24
• Total Time = 4.24 sec

∴ The total time taken for the sound to be heard is 4.24 sec

Answer 2

Given:-

• Initial velocity of Stone = 80m

• Height of Building = 80m

• Acceleration due to gravity = +10m/s²

• Speed of the Sound = 330m/s

To Find:-

• The Time when the Sound will be heard.

Formulae used:-

• s = ut + ½ × a × t²

• speed = Distance / time.

Now,

→ h = ut + ½ × a × t²

→ 80 = 0 × t + ½ × 10 × t²

→ 80 = 0 + 5t²

→ 80/5 = t²

→ 16 = t²

→ t = 4s.

The time taken by stone to reach the Pond is 4s.

we know that the sound will take time to produce.

Therefore,

→ speed = Distance / time

→ 330 = 80/t

→ t = 80/330

→ t = 8/33

→ t = 0.24

Therefore, The Sound of splash to reach the mouth of the Pond is 0.24s

Hence,

→ time when the sound will be heard = 4 + 0.24 → 4.24s

Hence, The time taken by sound to reach is 4.24s.