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Question

A stone is dropped from the top of a tower 500m high into a pond of water at the base of the tower. When is the splash heard at the top? Given, g=10ms-2 and speed of sound is 340ms-1


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Solution

Step 1: Given

Tower height = 500m

Speed of sound =340ms-1

Accleration due to gravity = g=10ms-2

Step 2. Find time taken to the stone to reach the tower's foundation.
According to the second equation of motion:

S=ut+12gt2

where,

u is the initial velocity

t is the time taken by an object to reach the final position.

gis the acceleration due to gravity.

Here, u is the stone's initial velocity u=0ms before falling

g=10m/s2 is the acceleration due to gravity.

and S is the distance traveled by the stone i.e. 500m which is the tower's height
Acceleration due to gravity, (g) is 10m/s2
t=t1 is the length of time it took the stone to reach the tower's foundation.

Put the above-given values Find the time takent=t1 by the stone to reach the base:
S=ut1+12gt12500=0×t1+12×10×t12t12=100t1=10s

Step 3. Find time taken by the sound of stone slashed in the pond to reach back to the top of the tower.

Time taken by the sound of stone slashed in the pond to reach back to the top of the tower (say t2) is:

t2=distancespeedofsound=500340=1.47s

Step 3. Find total time time taken after the stone is dropped to the sound of splash reached back.
Total time take taken after the stone is dropped to the sound of splash reached back:

t=t1+t2t=10+1.47t=11.47s

Therefore, the splash is heard at the top after 11.47s.


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