Hello All! I need help with this problem...
If a rock is is dropped from a cliff into an ocean, it travels approximately feet in seconds. If the splash is heard 4 seconds later and the speed of sound is 1100 ft./second, approximate the height of the cliff.
I thought the answer would just be: 4400 ft. I got a feeling I'm missing something. Any help would be great!
It takes the sound 4 seconds to be heard, so let be the time of fall and the amount of time it takes for the sound to travel up the cliff. Let the height of the cliff above the water be h.
Solve this system for h.
t1=x/16t...........1 , where t1(time taken by the stone to reach sea),16t(Speed of the stone)
t2=x/1100............2 , where t2(time taken by the sound to reach cliff)
from 1 and 2,we get t1+t2=x/16t+x/1100......3 and given t1+t2=4 seconds.
Therefore, eqn 3 changes to
4=x/16t+x/1100...........4 , which is a 2 variable eqn. so cannot be solved without a extra eqn. or we have to solve it by Hit and Trial or this Q. might have options to solve.
But it is sure x cannot be equal to 4400.(See the eqn. 4)
Taking t=1, and solving eqn 4, we will get,x=63.08 ft (approx)
Taking t=2, and solving eqn 4, we will get,x=124.38ft (approx)
Taking t=3, and solving eqn 4, we will get,x=183.97 ft (approx)
choose ur ans.