A stone dropped from the top of a tower of height 300 m 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 m s¯¹ ? (g = 9.8 m s¯²)
Given: The height of the tower is 300 m and the speed of sound in air is 340 m / s .
The distance travelled by the stone to reach the surface of the pond is,
s = u t 1 + 1 2 g t 1 2
where, t 1 is the time taken by the stone to reach the pond and u is the initial velocity of the stone.
The initial velocity of the stone is zero.
Rewrite the above equation as,
s = 1 2 g t 1 2 t 1 = 2 s g
By substituting the given values in the above equation, we get
t 1 = 2 ( 300 ) ( 9.8 ) = 7.82 s
The time taken by the sound to reach the height is given as,
t 2 = h v
By substituting the given values in the above equation, we get
t 2 = 300 340 = 0.88 s
The total time taken is given as,
t = t 1 + t 2
By substituting the given values in the above equation, we get
t = 7.82 + 0.88 = 8.7 s
Thus, the time taken by the sound of the splash to be heard is 8.7 s .
Given: The height of the tower is
The distance travelled by the stone to reach the surface of the pond is,
where,
The initial velocity of the stone is zero.
Rewrite the above equation as,
By substituting the given values in the above equation, we get
The time taken by the sound to reach the height is given as,
By substituting the given values in the above equation, we get
The total time taken is given as,
By substituting the given values in the above equation, we get
Thus, the time taken by the sound of the splash to be heard is
