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在讨论抛物体的射程这个问题中,一般的教科书只论及了这种情况:抛物体初速度v_0,以与水平面成夹角θ抛出。容易证明在这种情况下对应于最大射程的抛射角为45°。在日常生活中我们也会遇到这样的问题:在与水平面成α角的山脚下,以初速度v_0把物体向山坡上抛,为了在山坡上获得最大射程,应该以多大的倾角抛射呢?最大的射程与哪些因素有关呢?下面就来讨论这个问题。加附图所示,有一与水平面成α角的山坡OA,物体在O点以初速度v_0抛出,v_0与水平
In the discussion of the range of the parabolic body, the general textbook deals only with this situation: the initial velocity v_0 of the paraboloid is thrown at an angle θ from the horizontal plane. It is easy to prove that the projection angle corresponding to the maximum range in this case is 45°. In daily life, we will also encounter such a problem: At the foot of the mountain at an angle of α from the horizontal plane, we throw the object at the initial speed v_0 on the hillside. How much should we shoot with a large inclination in order to obtain the maximum range on the hillside? What are the factors related to the maximum range? Here’s a discussion of this issue. As shown in the drawing, there is a hillside OA with an angle α to the horizontal plane. The object is thrown at the initial velocity v_0 at point O, v_0 and horizontal