A Work and Projectile Question

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The discussion centers on a physics homework problem related to work and projectile motion. The participant is confused about why the velocity at half the maximum height is expressed as (Vo SQRT(2))/2, leading to a kinetic energy that is half of the initial energy. They note that this velocity corresponds to the sine and cosine of pi/4, but are seeking clarification on the reasoning behind the answer provided in the textbook. The focus remains solely on problem seven, with no further concern for question eight. Understanding the relationship between velocity and kinetic energy in projectile motion is essential for solving this problem.
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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
 

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