To determine the height of the cliff, we'll need to consider the time it takes for the sound to travel back up from the point of impact to the top of the cliff.
Let's break down the problem step by step:
1. Calculate the time it took for the rock to fall until it hit the water.
Since the sound is heard 3.7 seconds later, it means this is the total time it took for both the rock to fall and the sound to travel back up to the top of the cliff.
2. The speed of sound is given as 340 m/s, so we can use this value to calculate the distance traveled by sound during the 3.7 seconds it took to hear it.
Distance = Speed * Time
Distance = 340 m/s * 3.7 s
3. Now, we need to consider the time it took for the rock to fall. This is the time it took for the sound to travel back up, which we just calculated. So, to determine the time it took for the rock to fall until it hit the water, we can subtract this time from the total time of 3.7 seconds.
Time for rock to fall = Total time - Time for sound to travel back up
Time for rock to fall = 3.7 s - (distance/speed)
4. Next, we can calculate the distance fallen by the rock using the equation for free fall:
Distance = (1/2) * g * t^2
where g is the acceleration due to gravity (approximately 9.8 m/s^2) and t is the time for the rock to fall (which we calculated in the previous step).
5. Finally, we have the distance fallen by the rock, which is the same as the height of the cliff.
Let's calculate it:
Step 1:
Total time = 3.7 s
Step 2:
Distance = 340 m/s * 3.7 s = 1258 m
Step 3:
Time for rock to fall = 3.7 s - (1258 m / 340 m/s) = 3.7 s - 3.70 s = 0 s
Step 4:
Distance = (1/2) * 9.8 m/s^2 * (0 s)^2 = 0 m
Step 5:
The height of the cliff is 0 meters.
Therefore, the cliff has a height of 0 meters, which means the rock didn't actually have time to fall before hitting the water.