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

AI Thread Summary
The discussion centers on a potential error in an AP review book regarding the final speed of an object sliding down a frictionless ramp on a planet with double Earth's gravitational acceleration. The original equation used by the book, v = vo + (a)(t), is questioned for its applicability, with the poster suggesting that v² = (v0)² + (2)(a)(Δx) is more appropriate. By applying the latter equation with the adjusted gravitational acceleration, the poster concludes that the final speed should increase by a factor of √2, contradicting the book's claim of a final speed of 2. This discrepancy indicates a possible mistake in the review book's solution. The discussion highlights the importance of using the correct equations in physics problems.
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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