A rock is dropped from a 158-m-high cliff. How long does it take to fall (a) the first – Free 2B
A rock is dropped from a 158-m-high cliff. How long does it take to fall (a) the first 79.0 m and (b) the second 79.0 m ? (a) Number i Units (b) Number Units
Answer
Free Fall from a 158-meter Cliff – Physics Solution
This explanation uses kinematic equations to determine the time taken for an object in free fall to cover the first and second halves of a 158-meter drop.
Step 1: Time to Fall the First 79.0 m
d = (1/2) × g × t²
t = √(2d / g) = √(2 × 79.0 / 9.8) = √(16.1224) ≈ 4.015 s
t = √(2d / g) = √(2 × 79.0 / 9.8) = √(16.1224) ≈ 4.015 s
Time to fall the first 79.0 m = 4.015 seconds
Step 2: Time to Fall the Full 158.0 m
t = √(2 × 158.0 / 9.8) = √(32.2449) ≈ 5.678 s
Total time to fall 158.0 m = 5.678 seconds
Step 3: Time to Fall the Second 79.0 m
Δt = Total time − Time for first half = 5.678 s − 4.015 s = 1.663 s
Time to fall the second 79.0 m = 1.663 seconds
Final Summary
| Segment | Time (s) |
|---|---|
| First 79.0 m | 4.015 |
| Second 79.0 m | 1.663 |
| Total (158.0 m) | 5.678 |