college physics

tennis ball rolls off the edge of a tabletop 0.900m above the floor and strikes the floor at a point 1.60m horizontally from the edge of the table.

A: Find the time of flight of the ball

B: Find the magnitude of the initial velocity of the ball.

C: Find the magnitude of the velocity of the ball just before it strikes the floor.

D: Find the direction of the velocity of the ball just before it strikes the floor.

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  1. A. h = 0.5g*t^2 = 0.90 m.
    4.9t^2 = 0.90
    t^2 = 0.184
    t = 0.429 s. = Fall time.

    B. Dx = Xo*t = 1.6 m.
    Xo * 0.429 = 1.6
    Xo = 3.73 m/s. = Hor. component.

    C. Y = Yo+g*t = 0 + 9.8*0.429 = 4.20 m/s
    = Ver. component.

    V^2 = Xo^2 + Y^2 = 3.73^2 + 4.2^2=31.55
    V = 5.62 m/s.

    D. tan A = Y/Xo = 4.2/3.73 = 1.12601
    A = 48.4o. = Direction.

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  2. Distance covered along the pathway,
    s = sqrt(0.9^2 + 1.6^2) = 1.836 m
    Now, s = ut + ½*gt^2
    => 1.836 = 0.5 * 9.8 * t^2 [since u=0]
    => t = 0.612 sec (Fall time)

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