Two penguins are having fun sliding on an icy, nearly frictionless slope, that r

Question

Two penguins are having fun sliding on an icy, nearly frictionless slope, that rises above level ground at an angle of 10 degrees. One penguin has mass 18 kg while the other has mass 6 kg. At one point, the heavier penguin starting from rest, begins sliding frictionlessly down the slope. At the same time, the lighter penguin, starting from higher up the slope launches itself downward. It catches up to the heavier penguin after 2 seconds, both penguins then collide and, slide together down the hill. Immediately after the collision the pair of penguins is moving down the slope with a speed of 14 m/s.

What is the heavier penguin's momentum just before the collision? What was the lighter penguin's momentum just before colliding with the heavier one?  How fast did the lighter penguin launch itself down the slope? How much total impulse was exerted on the two penguins by gravity before the collision?

Explanation / Answer

The acceleration downwards is gsin10.

So, velocity attained by heavier penguin after 2 seconds is given by

v=0+ 9.8sin10*2

v= 3.403 m/s

Momentum= 18*3.403= 61.26 kgm/s.

Conserving momentum,

MV+ 61.26= (18+6)(14)

Momentum of lighter penguin is 274.74 kgm/s.

V= 274.74/6= 45.79m/s.

45.79= u+ 19.6*sin10

Impulse due to gravity is always zero.

u= 42.38m/s.

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