Conservation of Energy in Gravity

[college-kid]

Homework Statement

A boy at the top of a roller coaster falls through a vertical distance of 20m. What is the final speed of the boy if:
a) His initial speed was 0
b) His initial speed was 5 ms-1

Homework Equations

GPE at top = KE at bottom
mgh = 1/2mv^2
gh = 1/2v^2
v = √2gh

if the initial velocity (u) was not equal to zero, the maths becomes slightly different

initial total energy = final total energy
1/2mu^2 + mgh = 1/2mv^2

therefore...

v^2 = u^2 + 2gh

The Attempt at a Solution

a) 2x9.8x20 = 392

b) 5^2 + 2x9.8x20 = 417


The answers are:
a) 19.8 ms-1
b) 20.4 ms-1
What on Earth am I doing wrong... what can I do... or what? D: I just don't understand!

 

[kuruman]

If v²=392 m²/s², what is v?

 

[college-kid]

I love you and your wisdom. :D
Thankyou so much, you've really made my day!