A staircase contains three steps, each 10 cm high and 20 cm wide, as shown in the figure. Determine the minimum horizontal velocity, in m/s, of a ball rolling off the uppermost plane so that it directly hits the lowest plane.

Step-by-step solution

Let the edge of the uppermost plane be the origin (0,0) . The staircase has steps of height h = 10 cm = 0.1 m and width w = 20 cm = 0.2 m . From the given figure, to directly hit the lowest plane, the ball must clear the edge of the second step. The coordinates of the edge of the second step are x = 2w = 0.4 m and y = -2h = -0.2 m . The equation of the trajectory of the ball is given by: y = - gx^2 2u^2 For the ball to just clear the second step, its trajectory must pass through the point (0.4, -0.2) . Substituting