A body is projected up a smooth inclined plane (length =202m) with velocity u from the point M as shown in the figure. The angle of inclination is 45o and the top is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of v?

At point N, the angle of projection of the body will be 450.Let,the velocity of projection at this point is v. If the body just manages to cross the well, then Range = Diameter of well v2sin⁡2θg=40 As θ=45∘v2=400⇒v=20ms−1But we have to calculate the velocity (u) of the body at point M.For motion along the inclined plane (from M to N)Final velocity (v) = 20 ms,acceleration (a)=−gsin⁡α=−gsin⁡45∘, distance of inclined plane (s)=202m(20)=u2−2g2⋅202  Using v2=u2+2asu2=202+400⇒202m/s