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Answer 1

Given:

• As the pebble is dropped freely the initial velocity of the pebble is zero

• time taken by the pebble to reach the water surface= 20 sec

• acceleration due to gravity= 10 m /s²

• speed of sounds = 330 m/s

Solution :

As per the second kinematic equation

$\implies{h = ut + \frac{g{t}^{2} }{2} }$

here,

• h= depth of water
• u = initial velocity
• t = time taken
• a= acceleration due to gravity

Substituting the given values in the above equation we get ,

$\implies{h = \frac{g{t}^{2} }{2} }$

$\implies{h = \frac{10 \times 400}{2} }$

$\boxed{h = 2000m}$

we know that ,

$\implies{v = \frac{d}{t} }$

here ,

• v = velocity of sound
• d = h = depth of water
• t = time

$\implies{t = \frac{h}{v} }$

$\implies{t = \frac{2000}{330} }$

$\implies{t = 6.1s}$

time at which echo is heard after pebble is dropped

= time taken by the pebble to reach the bottom

+ time taken by the transverse wave to travel a distance of 2000 m

= 20 + 6.1

= 26.1 s

Answer:

• depth of the water surface= 2000 m
• time at which echo is heard after pebble is dropped = 26.1 sec

Answer 2

Given:

As the pebble is dropped freely the initial velocity of the pebble is zero

time taken by the pebble to reach the water surface= 20 sec

acceleration due to gravity= 10 m /s²

speed of sounds = 330 m/s

Solution :

As per the second kinematic equation

$\implies{h = ut + \frac{g{t}^{2} }{2} }$

here,

h= depth of water

u = initial velocity

t = time taken

a= acceleration due to gravity

Substituting the given values in the above equation we get ,

$\implies{h = \frac{g{t}^{2} }{2} }$

$\implies{h = \frac{10 \times 400}{2} }$

$\boxed{h = 2000m}$

we know that ,

$\implies{v = \frac{d}{t} }$

here ,

v = velocity of sound

d = h = depth of water

t = time

$\implies{t = \frac{h}{v} }$

$\implies{t = \frac{2000}{330} }$

$\implies{t = 6.1s}$

time at which echo is heard after pebble is dropped

= time taken by the pebble to reach the bottom

+ time taken by the transverse wave to travel a distance of 2000 m

= 20 + 6.1

= 26.1 s

Answer:

depth of the water surface= 2000 m

time at which echo is heard after pebble is dropped = 26.1 sec