1. The problem statement, all variables and given/known data An object is thrown with a ﬁxed initial speed v0 at various angles α relative to the horizon. At some constant height h above the launch point the speed v of the object is measured as a function of the initial angle α. Which of the following best describes the dependence of v on α? (Assume that the height h is achieved, and assume that there is no air resistance.) The answer is that v is independent of alpha. 2. Relevant equations v2 = (v_0cosθ)2 - 2gd Δx = v_ocosθt 3. The attempt at a solution Let the displacement be d, as mentioned in the problem. Solving for v gives: v = √(v_02cos2θ - 2gd) It looks like the velocity depends on the angle θ, particularly as θ increases, the velocity at that point seems to decrease. How/why is this wrong?