Question

The splash sound is heard 3 seconds after a stone is dropped from a bridge. Find the height of the bridge from the level of river water. [Take g=9.8 metre per second square] ​

Answer 1

Answer:

Let's assume that the stone takes (t) seconds to touch the water and another (t') seconds for the sound to reach our ears. It is given that all these processes happen within 3 seconds.

⇒ t + t' = 3

⇒ t' = (3 - t)   ...(1)

Now to find the distance from the top of the well, we use the second equation of motion. Hence we get:

⇒ s = ut + 0.5 at²

⇒ s = 0.5 (9.8) (t²)

(Since initial velocity is zero, ut = 0)

⇒ s = 4.9 t²   ...(2)

Now let us assume that the sound in air has a speed of 340 m/s.

The time taken for travelling the distance 's' in 340 m/s is given as:

⇒ t' = s/340

⇒ (3 - t) = s/340   ...(3)

Substituting the value of s = 4.9 t² in (3) we get:

⇒ (3 - t) = 4.9 t²/340

Cross multiplying we get:

⇒ 340(3 - t) = 4.9 t²

⇒ 1020 - 340t = 4.9 t²

⇒ 4.9 t² + 340t - 1020 = 0

Solving the above quadratic equation we get:

• t = 2.8
• t = -72.2

Since 't' cannot be negative, we ignore the second value.

Hence the time taken by the stone to touch the water is 2.8 seconds.

Distance from Bridge to River (s) = 4.9 (t²)

⇒ Depth = 4.9 × 2.8 × 2.8

⇒ Depth = 38.416 ≈ 38.4 m

Hence the height of the bridge from the level of river water is 38.4 m (approx).

Answer 2

Given :-

The splash sound is heard 3 seconds after a stone is dropped from a bridge.

To Find :-

Height of bridge from the level of river water.

Solution :-

Let the time taken by stone to touch ground be T

And when the sound come the time is t

T + t = 3

T = 3 - t (i)

Now

s = ut + 1/2 × at²

s = 0(t) + 1/2 × 9.8 × t²

s = 0 + 4.9t²

s = 4.9t²

Speed of sound in air is 340 m/s

Speed = Distance/Time

Time = Distance/Speed

T = 4.9t²/340

3 - t = 4.9t²/340

340(3 + t) = 4.9t²

1020 - 340t = 4.9t²

1020 - 340t - 4.9t² = 0

• Rearrange

4.9t² + 340t - 1020 = 0

Using quadratic equation

x = -b ± √b² - 4ac/2a

x = -340 ± √(340)² - 4(4.9)(-1020)/2(4.9)

x = -340 ± √115600 - (-19992)/9.8

x = -340 ± √1,35,592/9.8

x = -340 ± 368.2/9.8

x = 2.8

s = 4.9 t²

s = 4.9 × (2.8)²

s = 4.9 × 7.84

s = 38.4 m