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[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]​

Respuesta :

MathPhys

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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