Question

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.)

(A) v will increase monotonically with α.

(B) v will increase to some critical value v_max and then decrease.

(C) v will remain constant, independent of α.

(D) v will decrease to some critical value v_min and then increase.

(E) None of the above.

Answer 1

Correct option (C) v will remain constant, independent of α.

It’s a surprising result, but while both the horizontal and verticla components change at a given height with varying launch angle, the speed (v_x² + v_y²)^1/2 will be independent of α.