How Do You Calculate Displacement at Reduced Velocity in Free-Fall Motion?

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To calculate the displacement of a stone thrown upward at a reduced velocity of 5V, the initial upward distance is X when thrown at 10V. The equations of motion indicate that the stone's kinetic energy at half the speed results in it reaching only a quarter of the original height, suggesting it can ascend to 3/4 of X. The most efficient method to solve for displacement involves using kinematic equations, particularly considering the relationship between velocity, acceleration, and distance. The calculations confirm that the displacement at 5V is 0.75X. Understanding these principles is crucial for solving similar free-fall motion problems.
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Homework Statement



A stone is thrown straight upward with a velocity of 10V and travels upward a distance X. What is the displacement when the object is traveling at 5V?

Homework Equations



xf=x0+v0t+1/2at^2

vf=v0+at

vf^2=v0^2+2ax

The Attempt at a Solution



.75X? Further, what's the most efficient way of solving for it?
 
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With half the speed the stone has 1/4 of the kinetic energy left so can only go 1/4*X higher or it is at 3/4*X when the speed is 5V.
 
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