Easy-ish Conservation of Energy question

[elasticities]

Homework Statement

A waterfall has a change in elevation of 4.4*10^2 m. When the water has fallen 12% of its way to the bottom, its speed is 93m/s. Neglecting air resistance and fluid friction, determine the speed of the water at the top of the waterfall.

Homework Equations

Et1=Et2
Ek1+Eg1=Ek2+Eg2
1/2m(v1)^2+mgh1=1/2m(v2)^2+mgh2

The Attempt at a Solution

g=9.81 N/kg
v1=?
v2=93m/s
h1=440m
h2=440m*0.88=387.2m

1/2m(v1)^2+mgh1=1/2m(v2)^2+mgh2
1/2(v1)^2+gh1=1/2(v2)^2+gh2
1/2(v1)^2+(9.81)(440m)=1/2(93)^2+(9.81)(387.2m)

Am I doing it right so far?

 

[Doc Al]

So far, so good.

 

[elasticities]

1/2m(v1)^2+mgh1=1/2m(v2)^2+mgh2
1/2(v1)^2+gh1=1/2(v2)^2+gh2
1/2(v1)^2+(9.81)(440m)=1/2(93)^2+(9.81)(387.2m)
1/2(v1)^2+(4316.4)=4324.5+3798.432
1/2(v1)^2=3824.532
v1=87.5m/s

But this is not the answer in the answers section of the textbook.

 

[Doc Al]

The answer I get is very close to yours. (Just differs in the third digit.)

What textbook, by the way?

 

[elasticities]

The answer I get is very close to yours. (Just differs in the third digit.)

What textbook, by the way?

Maybe the answer is wrong in the textbook, it says 5m/s.
It's Nelson Physics 12 from 2003 I think.

 

[Doc Al]

Maybe the answer is wrong in the textbook, it says 5m/s.
It's Nelson Physics 12 from 2003 I think.

Sounds like the book messed up. If it started out at 5 m/s and fell the full 440 m, then it would have a speed of 93 m/s at the bottom.

 

[elasticities]

Sounds like the book messed up. If it started out at 5 m/s and fell the full 440 m, then it would have a speed of 93 m/s at the bottom.

Silly textbook, thanks though! :)