Question

If a stone is dropped into a lake from a tower, the sound of splash heard is by a man after 11.5s, then what is the height of the tower?

Answer 1

Let height of tower is h.

initial velocity of stone , u = 0

then time taken by the stone to reach the lake from tower is t

using formula, s = ut + 1/2 at²

or, h = 1/2gt² .....(1)

a/c to question, sound of splash heard is by a man after 11.5s.

so, time taken by sound to reach the man = (11.5 - t) sec

experimentally, speed of sound in air is 340 m/s

so, height of tower = time taken by sound to reach the man × speed of sound

h = (11.5 - t) × 340

from equation (1),

1/2 gt² = (11.5 - t) 340

or, t² = 68(11.5 - t)

t ≈ 10 sec

so, height of tower, h = 1/2 gt²

= 1/2 × 10 × 10²

= 500m

hence, answer is 500m

Answer 2

Answer:

Let height of tower is h.

initial velocity of stone , u = 0

then time taken by the stone to reach the lake from tower is t

using formula, s = ut + 1/2 at²

or, h = 1/2gt² .....(1)

a/c to question, sound of splash heard is by a man after 11.5s.

so, time taken by sound to reach the man = (11.5 - t) sec

experimentally, speed of sound in air is 340 m/s

so, height of tower = time taken by sound to reach the man × speed of sound

h = (11.5 - t) × 340

from equation (1),

1/2 gt² = (11.5 - t) 340

or, t² = 68(11.5 - t)

t ≈ 10 sec

so, height of tower, h = 1/2 gt²

= 1/2 × 10 × 10²

= 500m

hence the right answer is 500m