A Work and Projectile Question

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SUMMARY

The discussion centers on a physics homework problem regarding the relationship between kinetic energy and velocity at different heights during projectile motion. The user questions the reasoning behind the answer to problem seven, which states that the speed halfway to maximum height is (Vo SQRT(2))/2, leading to kinetic energy being half of its initial value. The user connects this velocity to trigonometric values of sin and cos at pi/4, seeking clarification on the derivation of the answer provided in the textbook.

PREREQUISITES
  • Understanding of basic physics concepts, particularly kinetic energy (K = mv²/2).
  • Familiarity with projectile motion and its equations.
  • Knowledge of trigonometric functions, specifically sine and cosine values.
  • Ability to interpret and analyze physics problems and solutions.
NEXT STEPS
  • Study the derivation of kinetic energy in relation to height in projectile motion.
  • Learn about the principles of energy conservation in physics.
  • Explore the relationship between velocity and height in projectile motion problems.
  • Review trigonometric identities and their applications in physics problems.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and projectile motion, as well as educators looking for clarification on common misconceptions in kinetic energy calculations.

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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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