I think my AP review book has an error. Can someone check?

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SUMMARY

The discussion centers on a physics problem regarding an object sliding down a frictionless ramp under different gravitational conditions. The original homework statement suggests using the equation v = vo + (a)(t), but participants argue that the equation v² = (v0)² + (2)(a)(Δx) is more appropriate for this scenario. When applying the latter equation with twice the gravitational acceleration (2g), the final speed increases by a factor of √2, contradicting the book's claim that the speed is 2. Thus, the book contains an error in its solution.

PREREQUISITES
  • Understanding of kinematic equations in physics
  • Knowledge of gravitational acceleration and its effects on motion
  • Familiarity with the concept of frictionless surfaces
  • Basic algebra for manipulating equations
NEXT STEPS
  • Review kinematic equations, particularly v² = (v0)² + (2)(a)(Δx)
  • Study the effects of varying gravitational acceleration on motion
  • Explore the principles of frictionless motion in physics
  • Investigate common errors in physics textbooks and how to identify them
USEFUL FOR

Students studying physics, educators reviewing textbook accuracy, and anyone interested in understanding motion under varying gravitational conditions.

Dennis Heerlein
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Homework Statement


An object of mass m is allowed to slide down a frictionless ramp of angle θ and its speed at the bottom is recorded as v. If this same process was followed on a planet with twice the gravitational acceleration as Earth, what would be its final speed?

Homework Equations


The book used v = vo + (a)(t) to solve, but since it's based on distance, isn't v2 = (v0)2 +(2)(a)(Δx) necessary to solve it?

The Attempt at a Solution


Using the latter equation, simply plugging in 2gsinθ instead of gsinθ, v will increase by a factor of √2; the book solution however says the answer is 2.
 
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