Max (15 kg) and Maya (12 kg) are ice-skating on a frozen pond. At one moment, when Max is skating away from the shore at 8.2 m/s and Maya is skating towards the shore at 4.6 m/s, they collide and bounce off each other without falling. If Maya rebounds at 3.4 m/s, what is Max's velocity after their collision?

Max (15 kg) and Maya (12 kg) are ice-skating on a frozen pond. When Max is standing on the shore, he throws a 1.5-kg snowball at Maya, who is standing at the center of the pond. Maya catches the snowball and she and the snowball move away from the shore at 2.0 m/s. How fast was the snowball moving right before Maya caught it?

Max (15 kg) and Maya (12 kg) are ice-skating on a frozen pond. While standing at the center of the pond, Maya throws a 1.5-kg snowball at Max and, as a result, recoils away from Max at 2.5 m/s. With what speed did Maya throw the snowball at Max?

a) Max's velocity after their collision = 1.8 m/s away from the shore

b) The snowball was moving 18 m/s

c) Maya threw the snowball with a velocity of 20 m/s at max

Explanation:

1) Max (15 kg) and Maya (12 kg) are ice-skating on a frozen pond. At one moment, when Max is skating away from the shore at 8.2 m/s and Maya is skating towards the shore at 4.6 m/s, they collide and bounce off each other without falling. If Maya rebounds at 3.4 m/s, what is Max's velocity after their collision?

m1*v1 + m2*V2 = m1*V1+m2+V2

⇒ with m1 = mass of max

⇒ with v1 = speed max is skating away = 8.2 m/s

⇒ with m2 = mass of Maya

⇒ with v2 = speed towards the shore Maya = - 4.6 m/s

⇒ with V1 = Max's veocity after the collision

⇒ with V2 = Maya's velocity after the collision = 3.4 m/s

Maya has a negative velocity before collision, because she is coming from the opposite direction. Her velocity after collision is positive because she rebounded, which means she went backwards, following the direction Max was coming from.

15kg * 8.2m/s + 12kg * - 4.6m/s = 15kg * V1 + 12kg * 3.4m/s

67.8 = 15V1 + 40.8

27 = 15V1

V1 = 1.8 m/s

Max's velocity after their collision = 1.8 m/s away from the shore

2) Max (15 kg) and Maya (12 kg) are ice-skating on a frozen pond. When Max is standing on the shore, he throws a 1.5-kg snowball at Maya, who is standing at the center of the pond. Maya catches the snowball and she and the snowball move away from the shore at 2.0 m/s. How fast was the snowball moving right before Maya caught it?

Let's consider away from Max as positive.

M1*v1 = (M1 + m2) * v2

⇒ with M1 = the mass of the snowball = 1.5 kg

⇒ with v1 = the velocity

⇒ with m2 = the mass of Maya = 12 kg

⇒ with v2 = velocity of Maya and the snowball = 2.0 m/s

1.5kg * v1 = (1.5 + 12) kg * 2m/s

1.51*v1 = 27

v1 = 18 m/s

The snowball was moving 18 m/s

Max (15 kg) and Maya (12 kg) are ice-skating on a frozen pond. While standing at the center of the pond, Maya throws a 1.5-kg snowball at Max and, as a result, recoils away from Max at 2.5 m/s. With what speed did Maya throw the snowball at Max?

Consider the direction 'to Max' as positive and away from Max as negative.

m1*v1 + m2*v2 = 0

⇒ with m1 = the mass of Maya = 12 kg

⇒ with v1 = the velocity of Maya = - 2.5 m/s

⇒ with m2 = thz mass of the snowball = 1.5 kg

⇒ with v2 = the velocity of the snowball

12kg * - 2.5m/s + 1.5kg * V = 0

-30 = - 1.5V

V = 20 m/s

Maya threw the snowball with a velocity of 20 m/s at max