Thomas threw a ball down a pit that was 400m deep. a) How long did it take to land? b) What speed was it going when it landed?​

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