Final answer:
The height of the cliff is 425 meters. This is calculated by halving the total distance sound traveled (850 meters) on a round trip (to the cliff and back) in the given 2.5 seconds at a speed of 340 m/s.
Step-by-step explanation:
To calculate the height of the cliff, we first need to understand that the sound travels from the person whistling, to the cliff, and back to the person's ears in 2.5 seconds. Since the speed of sound is given as 340 m/s, we can use the formula distance = speed × time. However, this time should be halved, as it includes the time to reach the cliff and the time to return.
First, we calculate the total distance traveled by the sound:
- Total distance = speed of sound × time
- Total distance = 340 m/s × 2.5 s
- Total distance = 850 meters
Since this distance is a round trip, we divide it by 2 to find the one-way distance to the cliff (which is the same as the height of the cliff in this scenario):
- Height of the cliff = Total distance / 2
- Height of the cliff = 850 meters / 2
- Height of the cliff = 425 meters
Therefore, the height of the cliff is 425 meters.