Romeo is chucking pebbles gently up to Juliet\'s window, and hewants the pebbles

Question

Romeo is chucking pebbles gently up to Juliet's window, and hewants the pebbles to hit the window with only a horizontalcomponent of velocity. He is standing at the edge of a rose garden4.5m below her window and 5.0m from the base of the wall. How fastare the pebbles going when they hit her window?
This is the diagram they show: Romeo is chucking pebbles gently up to Juliet's window, and hewants the pebbles to hit the window with only a horizontalcomponent of velocity. He is standing at the edge of a rose garden4.5m below her window and 5.0m from the base of the wall. How fastare the pebbles going when they hit her window?
This is the diagram they show:

Explanation / Answer

    Vertical distance, Y = 4.5 m     Horizontal range, R = 5 m     Let         Initial velocity of projection = U     Vertical component of initial velocity = Uy     Vertical component of final velocity, Vy = 0m/s     Horizontal component of initial velocity =Ux     Horizontal component of final velocity , Vx =Ux               ( since Vy = 0 )     Vertical motion:     V2 - U2 = 2 a S     Vy 2 - Uy 2 = 2 * - g *Y     0 - Uy 2 = - 19.6 * 4.5     Vertical component of initial velocity, Uy =9.39 m/s     Angle made when hitting the window, =0o ( horizontal )     Tan = Vy / Vx     0 = Uy - gt / Ux     Uy - gt = 0     g t = Uy     time, t = Uy / g              = 9.39 / 9.8              = 0.958 s     Horizontal range, R = Ux t           5 = Ux * 0.958     Horizontal component of initial velocity, Ux =5.22 m/s     Horizontal component of final velocity , Vx = Ux= 5.22 m/s     Final Velocity of pebbles, V = Vx = 5.22 m/s (horizontal )

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