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?

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.