A mother has four times the mass of her young son. Both are running with the same kinetic energy. What is the ratio vs/vm other of their speeds?

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**Problem Statement:**

A mother has four times the mass of her young son. Both are running with the same kinetic energy.

**Question:**

*Part A*

What is the ratio \( v_s / v_m \) of their speeds?

\[ v_s / v_m = \]

**Explanation:**

This problem involves understanding the relationship between mass, speed, and kinetic energy. According to the kinetic energy formula, \( KE = \frac{1}{2}mv^2 \), when two objects have the same kinetic energy, their speeds relate inversely to the square root of their masses.

Given:
- The mother’s mass \( m_m = 4m_s \) (four times the son's mass).
- Kinetic energy \( KE_m = KE_s \).

You need to find the speed ratio \( v_s / v_m \).
Transcribed Image Text:**Problem Statement:** A mother has four times the mass of her young son. Both are running with the same kinetic energy. **Question:** *Part A* What is the ratio \( v_s / v_m \) of their speeds? \[ v_s / v_m = \] **Explanation:** This problem involves understanding the relationship between mass, speed, and kinetic energy. According to the kinetic energy formula, \( KE = \frac{1}{2}mv^2 \), when two objects have the same kinetic energy, their speeds relate inversely to the square root of their masses. Given: - The mother’s mass \( m_m = 4m_s \) (four times the son's mass). - Kinetic energy \( KE_m = KE_s \). You need to find the speed ratio \( v_s / v_m \).
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