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

[Dennis Heerlein]

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 = v_o + (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.

 

[Nathanael]

I agree with you.