We can solve this problem using the principles of conservation of momentum. Since the collision is elastic, both momentum and kinetic energy are conserved.

Step 1: Understanding the situation

• Mass of the goalie: $m_g = 70.0 \, \text{kg}$
• Mass of the puck: $m_p = 0.150 \, \text{kg}$
• Initial velocity of the goalie: $v_{g,i} = 0 \, \text{m/s}$ (since the goalie is initially at rest)
• Initial velocity of the puck: $v_{p,i} = 35.0 \, \text{m/s}$
• Final velocity of the puck: Since the puck is reflected in the opposite direction, its final velocity is $v_{p,f} = -35.0 \, \text{m/s}$.

Step 2: Conservation of momentum

The total momentum before the collision must equal the total momentum after the collision. This is expressed as:

$m_g \cdot v_{g,i} + m_p \cdot v_{p,i} = m_g \cdot v_{g,f} + m_p \cdot v_{p,f}$

Substitute the known values into the equation:

$70.0 \cdot 0 + 0.150 \cdot 35.0 = 70.0 \cdot v_{g,f} + 0.150 \cdot (-35.0)$

$0 + 5.25 = 70.0 \cdot v_{g,f} - 5.25$

$5.25 + 5.25 = 70.0 \cdot v_{g,f}$

$10.5 = 70.0 \cdot v_{g,f}$

Step 3: Solve for $v_{g,f}$

$v_{g,f} = \frac{10.5}{70.0}$

$v_{g,f} = 0.150 \, \text{m/s}$

Final Answer:

The final velocity of the goalie is $0.150 \, \text{m/s}$.

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Would you like any further explanation on this, or would you like to go deeper into the elastic collision concepts?

Here are some additional related questions you might find interesting:

1. How would the final velocity of the goalie change if the collision was inelastic?
2. What would happen to the final velocities if the goalie had a different mass?
3. How does the concept of elastic collisions apply to real-world scenarios like a puck hitting a glass wall?
4. How would you calculate the final kinetic energy after the collision in this case?
5. What are the differences between elastic and inelastic collisions in terms of momentum and energy?

Tip: Always check the conditions of the problem carefully—such as whether the collision is elastic or inelastic—because that determines whether energy is conserved along with momentum.