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26 September, 19:03

A 15.0 kg penguin waddling east at a velocity of 7.0 m/s collides with a stationary 10.0 kg penguin. After the collision the 15.0 kg penguin is traveling at a velocity of 4.2 m/s 20.0 degrees S of E.

a. What is the velocity of the 10.0 kg penguin after collision?

b. is this collision elastic or inelastic? if inelastic, what is the energy loss?

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  1. 26 September, 20:54
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    Part A:

    Using momentum conservation we have:

    Direction x:

    (15) (7.0) + 0 = (15) (4.2) cos (-20 °) + (10) v₂ (f) cosθ

    (10) v₂ (f) cosθ = (15) (7.0) - (15) (4.2) cos (-20 °) ... (Eq 1)

    Direction y:

    0 + 0 = (15) (4.2) sin (-20 °) + (10) v₂ (f) sinθ

    (10) v₂ (f) sinθ = - (15) (4.2) sin (-20 °) ... (Eq 2)

    We divide both equations (1) and (2):

    Left side:

    (10) v₂ (f) sinθ / (10) v₂ (f) cosθ = tanθ

    Right side:

    - (15) (4.2) sin (-20 °) / (15) (7.0) - (15) (4.2) cos (-20 °)

    Clearing the angle we have:

    θ = tan⁻¹ [ - (15) (4.2) sin (-20 °) / (15) (7.0) - (15) (4.2) cos (-20 °) ]

    θ = 25 °

    We use any of the equations to find the speed.

    From (2) we have:

    (10) v₂ (f) sinθ = - (15) (4.2) sin (-20 °)

    v₂ = - (15) (4.2) sin (-20 °) / (10) sin25 °

    Answer:

    v₂ = 5.1m / s

    Note:

    θ = 25 ° (direction is in the first quadrant, north of east)

    Part B:

    Initial kinetic energy:

    K (i) = 0.5 (15) (7.0) ²

    = 370J (rounded)

    Final kinetic energy:

    KE (f) = 0.5 (15kg) (4.2m / s) ² + 0.5 (10kg) (5.1m / s) ²

    = 260J (rounded)

    Answer:

    A difference of 110J, so it was an inelastic collision.
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