In a ballistic pendulum experiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile (of the

Question

In a ballistic pendulum experiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile (of the same mass) causes the the pendulum to swing twice as high, 5.2 cm. The second projectile was how many times faster than the first?

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Thạch Thảo 2 months 2021-07-30T01:35:47+00:00 1 Answers 3 views 0

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    2021-07-30T01:37:24+00:00

    Answer:

    The second projectile is \sqrt{2} times faster than the first projectile.

    Explanation:

    Mass of first projectile = m

    height h_{1} = 2.6 cm

    Height H_{2} = 5.2 cm

    Let velocity of first projectile = V

    Velocity of first projectile = V’

    From conservation of momentum principal

    m V = (m + m) V’

    V = \frac{m +m}{m} V'

    V’ = \sqrt{2gH}

    V = \frac{m +m}{m} \sqrt{2gH}

    Therefore velocity is directly proportional to the height.

    \frac{V_{2} }{V_{1} } =\frac{ \sqrt{H_{2} } }\sqrt{H_{1}

    Since H_{2} = 2 H_{1}

    \frac{V_{2} }{V_{1} } = \sqrt{2}

    Therefore the second projectile is \sqrt{2} times faster than the first projectile.

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