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Example of two dimensional motions Question : A very broad elevator is going up vertically with a constant acceleration of 2 ms -2 . At the instant when its velocity is   4ms -1 a ball is projected from the floor of the lift with a speed of 4ms -1 relative to the floor at an elevation of 30ᵒ . If g = 10 ms -1   , find (a) the time taken by the ball to return to the floor. (b) The range of the ball over the floor of the lift. Solution : Here , u = 4 m/s, θ = 30ᵒ. Acceleration of the ball relative to the lift =10+2 = 12 m/s 2 Acting in the negative y-direction or vertically downwards.   It means’ Here    g’=12 m/s 2 Time of flight, T = 2u sin θ /g’=2 × 4 × sin30ᵒ/12=1/3 s Horizontal range, R = u 2 sin 2θ /g’= (4) 2 sin 2 × 30ᵒ/12= 1.15 m   Question : A cannon ball has the range R, for two angles of projection. If the maximum height attained are H and H’ respectively and t and t’ be the respective times of flight in two possible pat...