(Solved) Explain why initial velocity in trajectory motion is equal to the final velocity?

Rkamu

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11 years ago

Explain why initial velocity in trajectory motion is equal to the final velocity?

I'm in AP Physics and am struggling with this concept! Can someone please help me? I understand that trajectory motion can be shown using a parabola, and therefore both initial and final velocity would have the same y-value. However, that is as far as my teacher got in explaining it. Can someone explain why the y-values would be equal?

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bugg

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11 years ago

Well just think of it like this. the hight that a projectile reaches is equal to the amount of energy that the force of gravity has taken away from it. it reaches its maximum height (it is instantaneously motionless) when the force of gravity has taken away all the kinetic energy associated with it.

now when the projectile falls back the force of gravity must give it the same amount of kinetic energy it removed from it at its initial height. Its just the law of conservation of energy.

hope this helps.

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rkearl27

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11 years ago

This verified answer contains over 340 words.

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rnb121

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11 years ago

Look at the equations of motion

D = 0.5at^2 + Vo*t
V = at + Vo

Nlye that there is no direction term. That means that up is the same as down. Gravity acts only vertically. Thus, time, acceleration up are equal to time, acceleration down. That means the vertical component of velocity when the projectile returns to earth must be equal to the vertical component of the original velocity.

There are assumed no forces acting horizontally so by Newtons 1st Law the hotlrizontal component of the original velocity does not change

If horizontal and vertical components are the same then the resultant must also be the same

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