A 35 g steel ball is held by a ceiling-mounted electromagnet 4.0 m above the floor. A compressed-air cannon sits on the floor, 4.4 m to one

Question

A 35 g steel ball is held by a ceiling-mounted electromagnet 4.0 m above the floor. A compressed-air cannon sits on the floor, 4.4 m to one side of the point directly under the ball. When a button is pressed, the ball drops and, simultaneously, the cannon fires a 25 g plastic ball. The two balls collide 1.2 m above the floor. What was the launch speed of the plastic ball?

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Sapo 3 years 2021-08-15T20:38:22+00:00 1 Answers 38 views 0

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  1. ThanhThu
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    2021-08-15T20:40:05+00:00
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    Answer:

    7.9 m/s

    Explanation:

    When both balls collide, they have spent the same time for their motions.

    Motion of steel ball

    This is purely under gravity. It is vertical.

    Initial velocity, u = 0 m/s

    Distance, s = 4.0 m – 1.2 m = 2.8 m

    Acceleration, a = g

    Using the equation of motion

    s = ut+\frac{1}{2}at^2

    2.8 \text{ m} = 0+\dfrac{gt^2}{2}

    t = \sqrt{\dfrac{5.6}{g}}

    Motion of plastic ball

    This has two components: a vertical and a horizontal.

    The vertical motion is under gravity.

    Considering the vertical motion,

    Initial velocity, u = ?

    Distance, s = 1.2 m

    Acceleration, a = –g                   (It is going up)

    Using the equation of motion

    s = ut+\frac{1}{2}at^2

    1.2\text{ m} = ut-\frac{1}{2}gt^2

    Substituting the value of t from the previous equation,

    1.2\text{ m} = u\sqrt{\dfrac{5.6}{g}}-\dfrac{1}{2}\times g\times\dfrac{5.6}{g}

    u\sqrt{\dfrac{5.6}{g}} = 4.0

    Taking g = 9.8 m/s²,

    u = \dfrac{4.0}{0.756} = 5.29 \text{ m/s}

    This is the vertical component of the initial velocity

    Considering the horizontal motion which is not accelerated,

    horizontal component of the initial velocity is horizontal distance ÷ time.

    u_h = \dfrac{4.4\text{ m}}{0.756\text{ s}} = 5.82\text{ m/s}

    The initial velocity is

    v_i = \sqrt{u^2+u_h^2} = \sqrt{(5.29\text{ m/s})^2+(5.82\text{ m/s})^2} = 7.9 \text{ m/s}

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