一道大学英文数学题求解
是一道MODELLING AND DYNAMICS的题
An inclined plane passes through the origin and makes an angle β>0 with the horizontal.A ball is thrown from the origin up the plane with speed V at an angle α>β to the horizontal.
i)Find x(t),the path of the ball,assuming that the only force acting on the ball is its weight,vertically downwards.
ii)Show that the ball lands on the plane at time t=2Vsin(α-β)/(gcosβ).
iii)Find the range r of the ball(i.e.the distance from the origin to the point at which the ball lands on the plane).
iv)Show that the maximum range is achieved when α bisects the angle between the plane and the vertical,and that the maximum range is V平方/[g(1+sinβ)].