College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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### Problem Statement

You are standing on a very slippery icy surface and throw a 1 kg football horizontally at a speed of **4.5 m/s**. What is your velocity (in m/s) when you release the football? (Assume your mass is **66 kg** and that the positive direction is the direction of motion of the football. Indicate the direction with the sign of your answer.)

- **Your velocity:**
  \[ \_\_\_\_\_\_\_\_ \] m/s

---

### Explanation:

This is a physics problem involving the conservation of momentum. When you throw the football on an icy surface, your velocity is affected in the opposite direction due to the conservation of momentum principle, which states that the total momentum of a closed system remains constant if no external forces act on it. 

Given:
- Mass of football (m_f): 1 kg
- Speed of football (v_f): 4.5 m/s
- Your mass (m_y): 66 kg

The equation for conservation of momentum before and after the throw is:
\[ m_y \cdot v_y = - m_f \cdot v_f \]

where:
- \( v_y \) is your velocity to be determined.

Solving for \( v_y \):
\[ 66 \cdot v_y = - 1 \cdot 4.5 \]
\[ v_y = - \frac{4.5}{66} \]
\[ v_y \approx -0.0682 \, \text{m/s} \]

Your velocity will be **-0.0682 m/s** in the direction opposite to the football's motion.

---

This explanation can be used to help students understand the principles behind the problem and how to apply them to solve for the unknown variable.
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Transcribed Image Text:--- ### Problem Statement You are standing on a very slippery icy surface and throw a 1 kg football horizontally at a speed of **4.5 m/s**. What is your velocity (in m/s) when you release the football? (Assume your mass is **66 kg** and that the positive direction is the direction of motion of the football. Indicate the direction with the sign of your answer.) - **Your velocity:** \[ \_\_\_\_\_\_\_\_ \] m/s --- ### Explanation: This is a physics problem involving the conservation of momentum. When you throw the football on an icy surface, your velocity is affected in the opposite direction due to the conservation of momentum principle, which states that the total momentum of a closed system remains constant if no external forces act on it. Given: - Mass of football (m_f): 1 kg - Speed of football (v_f): 4.5 m/s - Your mass (m_y): 66 kg The equation for conservation of momentum before and after the throw is: \[ m_y \cdot v_y = - m_f \cdot v_f \] where: - \( v_y \) is your velocity to be determined. Solving for \( v_y \): \[ 66 \cdot v_y = - 1 \cdot 4.5 \] \[ v_y = - \frac{4.5}{66} \] \[ v_y \approx -0.0682 \, \text{m/s} \] Your velocity will be **-0.0682 m/s** in the direction opposite to the football's motion. --- This explanation can be used to help students understand the principles behind the problem and how to apply them to solve for the unknown variable.
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