To solve this problem, we need to determine the distance from the hunter to the cliff using the time it took for the echo to return and the speed of sound.

Given:

• Time taken for the echo to be heard after the shot is fired: $t = 8$ seconds
• Speed of sound: $v = 320 \, \text{m/s}$

Concept:

The sound travels from the hunter to the cliff and then back to the hunter, so the total distance covered by the sound is twice the distance from the hunter to the cliff.

Let:

• $d$ be the distance from the hunter to the cliff.

The sound travels this distance twice, so: $\text{Total distance} = 2d$

Using the formula for distance: $\text{Distance} = \text{Speed} \times \text{Time}$

So, the total distance covered by the sound is: $2d = v \times t$

Plugging in the given values: $2d = 320 \, \text{m/s} \times 8 \, \text{s}$ $2d = 2560 \, \text{m}$

Now, solve for $d$: $d = \frac{2560 \, \text{m}}{2}$ $d = 1280 \, \text{m}$

Answer:

The distance of the hunter to the cliff is $\boxed{1280 \, \text{m}}$, which corresponds to option D.

Would you like to go over the details, or do you have any questions?

Additional Questions:

1. How would the answer change if the speed of sound was different?
2. What happens to the distance if the time taken for the echo increases?
3. Can you calculate the distance if the hunter heard the echo in 6 seconds instead of 8?
4. How would wind speed affect the results of this calculation?
5. What other factors could influence the speed of sound in real-world conditions?

Tip:

When dealing with echo problems, remember that the sound travels to the reflecting surface and back, so you always need to account for the round-trip distance!