A Work and Projectile Question

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Homework Statement

http://img528.imageshack.us/img528/9549/87609045.jpg

Homework Equations

W = delta K

The Attempt at a Solution

ok I have a question about these problems, except for 8. For number seven the answer in the back of the book is B. This led me to believe that the speed half way up to it's max height is

( Vo SQRT(2) )/2

pluging this value into the velocity for kinetic energy

K = (mv^2)/2 allows for the kinetic energy to be half it's intial...

so my question is why? Why is it's velocity SQRT(2)/2 it's intial? I realized that this value is the exact value for sin and cos pi/4... I can not understand why the answer is B

Don't WORRY ABOUT QUESTION 8 I GOT IT

 

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Please I still don't understand 7