[9] (b) A billiard ball B at rest is struck by an identical ball A moving with a speed of 10 m/s along the positive y-axis. After

Question

[9]
(b) A billiard ball B at rest is struck by an identical ball A moving with a speed of 10 m/s along
the positive y-axis. After the collision, the two balls move off in directions that are perpendicular
to each other, with ball A making 15° with the positive y-axis. Find the final velocities (Direction
and magnitude) of both balls. [16]​

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Xavia 5 years 2021-08-03T18:28:45+00:00 1 Answers 37 views 0

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  1. quangkhai
    0
    2021-08-03T18:30:44+00:00
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    Answer:

    9.66 m/s 15° with +y

    2.59 m/s 75° with +y

    Explanation:

    Momentum is conserved in the y direction.

    mu₁ + mu₂ = mv₁ + mv₂

    u₁ + u₂ = v₁ + v₂

    10 m/s + 0 m/s = v₁ cos 15° + v₂ cos 75°

    10 = v₁ cos 15° + v₂ cos 75°

    Momentum is conserved in the x direction.

    mu₁ + mu₂ = mv₁ + mv₂

    u₁ + u₂ = v₁ + v₂

    0 m/s + 0 m/s = v₁ sin 15° − v₂ sin 75°

    0 = v₁ sin 15° − v₂ sin 75°

    v₁ sin 15° = v₂ sin 75°

    v₂ = v₁ sin 15° / sin 75°

    Substitute.

    10 = v₁ cos 15° + (v₁ sin 15° / sin 75°) cos 75°

    10 = v₁ cos 15° + v₁ sin 15° / tan 75°

    10 = v₁ (cos 15° + sin 15° / tan 75°)

    v₁ ≈ 9.66 m/s

    v₂ ≈ 2.59 m/s

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