Ice-hockey star Wayne Gretzky is skating at 12.7 m/s toward a defender, who in turn is skating at 5.39 m/s toward Gretzky. Gretzky’s weight is 677 N; that of the defender is 869 N. Immediately after the collision, Gretzky is moving at 2.21 m/s in his original direction. You can ignore external horizontal forces applied by the ice to the skaters during the collision. What is the velocity of the defender immediately after the collision?

Give your answer in m/s to the second decimal place.

Hint: Take Gretzky’s initial direction as the positive velocity.

initial momentum in + x direction =

677/g * 12.7 - 869/g * 5.39
= +3914/g
final momentum in + x direction = 677/g * 2.21 + 869/g * V
= +1496/g + 869/g * V
so
3914 = 1496 + 869 * V
2418 = 869 V
V = + 2.78
Wayne Won

Wonderful explanation keep it up

To solve this problem, we can use the principle of conservation of momentum.

The momentum before the collision is equal to the momentum after the collision.

The momentum of an object is given by the product of its mass and velocity.

Let's denote Gretzky's mass as m1 and the defender's mass as m2.

Given:
Gretzky's initial velocity (before the collision) = 12.7 m/s
Defender's initial velocity (before the collision) = -5.39 m/s (negative as the defender is moving toward Gretzky)
Gretzky's final velocity (after the collision) = 2.21 m/s
Defender's final velocity (after the collision) = v2 (unknown)

The momentum before the collision: p_initial = m1 * v1 + m2 * v2

The momentum after the collision: p_final = m1 * v_final + m2 * v2

We can set these two equations equal to each other: p_initial = p_final

m1 * v1 + m2 * v2 = m1 * v_final + m2 * v2

Substituting the given values into the equation:
(677 N) * (12.7 m/s) + (869 N) * (-5.39 m/s) = (677 N) * (2.21 m/s) + (869 N) * v2

Simplifying the equation:
(8627.9 N * m/s) - (4691.91 N * m/s) = (1496.17 N * m/s) + (869 N * v2)

3936.99 N * m/s = 1496.17 N * m/s + 869 N * v2

3936.99 N * m/s - 1496.17 N * m/s = 869 N * v2

2440.82 N * m/s = 869 N * v2

Dividing both sides by 869 N:
v2 = (2440.82 N * m/s) / 869 N

v2 ≈ 2.81 m/s

Therefore, the velocity of the defender immediately after the collision is approximately 2.81 m/s.

To solve this problem, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object is calculated by multiplying its mass by its velocity. In this case, we are given the weights of both Gretzky and the defender, but we are not told their masses. However, we can use the weight and the acceleration due to gravity to find the mass of each player.

The weight of an object can be calculated using the equation:

Weight = mass * gravity

where gravity is approximately 9.8 m/s^2.

Solving for the mass of Gretzky, we have:

677 N = mass of Gretzky * 9.8 m/s^2

mass of Gretzky = 677 N / 9.8 m/s^2

Similarly, for the mass of the defender:

869 N = mass of the defender * 9.8 m/s^2

mass of the defender = 869 N / 9.8 m/s^2

Now that we have the masses of the two players, we can proceed to calculate their momenta before and after the collision.

The momentum of an object is given by the equation:

Momentum = mass * velocity

Before the collision, the momentum of Gretzky is:

Momentum of Gretzky before collision = mass of Gretzky * velocity of Gretzky (positive, as stated in the hint)

And the momentum of the defender is:

Momentum of the defender before collision = mass of the defender * velocity of the defender (negative, as the defender is moving in the opposite direction)

Now, since the total momentum is conserved, we have:

Total momentum before collision = Total momentum after collision

Momentum of Gretzky before collision + Momentum of the defender before collision = Momentum of Gretzky after collision + Momentum of the defender after collision

Plugging in the given values and the calculated masses, and rearranging the equation to solve for the velocity of the defender after the collision, we have:

mass of Gretzky * velocity of Gretzky + mass of the defender * velocity of the defender = mass of Gretzky * velocity of Gretzky (after collision) + mass of the defender * velocity of the defender (after collision)

Solve this equation for the velocity of the defender after the collision, and round your answer to the second decimal place.