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7 September, 07:29

You and a friend stand on a snow-covered roof. you both throw snowballs from an elevation of 15 m with the same initial speed of 13 m/s, but in different directions. you throw your snowball downward, at 40° below the horizontal; your friend throws her snowball upward, at 40° above the horizontal. what is the speed of each ball when it is 5.0 m above the ground? (neglect air resistance.)

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  1. 7 September, 10:05
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    Refer to the diagram shown below.

    g = 9.8 m/s², and air resistance is ignored.

    Let us consider the two trajectories.

    Case A; The ball is launched 40° below the horizontal

    u = (13 m/s) * cos 40° = 9.9586 m/s, the horizontal velocity

    v = - (13 m/s) * sin 40° = - 8.3562 m/s

    When the ball is at 5 m above ground, it would have traveled 10 m.

    The vertical downward velocity is

    V² = (-8.3562 m/s²) ² + 2 * (-9.8 m/s²) * (-10 m) = 265.826

    V = + / - 16.304 m/s = > V = - 16.304 m/s (downward)

    The horizontal velocity remains unchanged.

    The speed of the ball is

    √[ (-16.304) ² + 9.9586²] = 19.105 m/s

    Case B: The ball is launched 40° above the horizontal.

    u = 9.9586 m/s, as in case A

    v = 8.3562 m/s

    When the ball is 5 m above ground, the vertical velocity, V, is given by

    V² = (8.3562 m/s) ² + 2 * (-9.8 m/s²) * (-10 m) = 265.826

    V = + / - 16.304 m/s

    The speed of the ball is

    √[ (-16.304) ² + 9.9586²] = 19.105 m/s

    Surprisingly, both speeds are the same.

    Answer:

    The speed of the ball when it is 5 m above ground is 19.1 m/s (both cases).
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