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原题某游乐园入口旁有一喷泉,喷出的水柱将一质量为M的卡通玩具稳定地悬停在空中。为计算方便起见,假设水柱从横截面积为S的喷口持续以速度v_0竖直向上喷出;玩具底部为平板(面积略大于S);水柱冲击到玩具底板后,在竖直方向水的速度变为零,在水平方向朝四周均匀散开。忽略空气阻力。已知水的密度为ρ,重力加速度大小为g。求:(i)喷泉单位时间内喷出的水的质量;(ii)玩具在空中悬停时,其底面相对于喷口的高度。题文中的“玩具底部平板(面积略大于S)”这一条件是有
The original title of an amusement park next to a fountain, the jet of water will be a mass of M cartoon toys steady hovering in the air. For convenience of calculation, it is assumed that the water column is sprayed vertically upwards from a spout of cross-sectional area S at speed v_0; the bottom of the toy is a flat plate (the area is slightly larger than S); the speed of the water in the vertical direction after the water column impacts the toy floor Become zero and spread evenly around in the horizontal direction. Ignore the air resistance. It is known that the density of water is ρ and the magnitude of gravitational acceleration is g. (I) The mass of water ejected during a unit of time; (ii) The height of the bottom of the toy relative to the spout when hovering in the air. The inscription “toy bottom plate (area slightly larger than S) ” This condition is there