A stone is dropped into a bore well 490m deep.after how time,the sound of splash of will be heard
time=timetofall+timesoundup
falling:
490=1/2 g t^2 or
t=sqrt(2*490/g)
soundup:
490=vsound*time
time=490/vsound
To find the time it takes for the sound of the splash to be heard, we need to calculate the time it takes for the stone to fall to the bottom of the bore well.
We can use the equation of motion:
s = ut + (1/2)at^2
where:
s = distance fallen (490m)
u = initial velocity (0, as the stone is dropped, not thrown)
a = acceleration due to gravity (-9.8 m/s^2, assuming the stone is in freefall)
Rearranging the equation, we get:
s = (1/2)at^2
Simplifying, we have:
490 = (1/2)(-9.8)t^2
Now, let's solve for t:
490 = -4.9t^2
Divide both sides by -4.9:
t^2 = -100
Since the equation has a negative value on the right side, this indicates that there is no real solution for t. Therefore, the stone will not reach the bottom of the bore well and no sound of the splash will be heard.
It's important to note that we assumed no air resistance in this calculation. In reality, air resistance would affect the stone's fall and the subsequent sound heard.