Hi there!
a)
We can use the equation t = √2d/g to solve. (Let's let g = 10 m/s²)
**How to get this equation**
We have the equation:
Δd = vit + 1/2at²
For freefall, we know that vi = 0, so we are left with:
Δd = 1/2at²
We know that a = g. Rearrange in terms of t:
2Δd / a = t²
Square root both sides:
√(2d/a) = t
Plug in the height and gravity:
t = √2(400)/10 = √800/10 = √80 ≈ 8.94 sec
b)
Find the final speed using the following formula:
vf = √2gd
**How to derive**
We know the equation:
vf² = vi² + 2ad
vi = 0, so:
vf² = 2ad
Square root both sides:
vf = √2ad
vf = √2(400)(10) = √8000 ≈ 89.44 m/s