Two iceboats (one of mass m, one of mass 2m) hold a race on a frictionless, horizontal, frozen lake. Both i iceboats start from rest, and the wind exerts the same constant force on both iceboats. Which iceboat crosses the finish line with more kinetic energy (KE)? Start Finish O The iceboat of mass 2m: it has four times as much KE as the other. O The iceboat of mass m: it has four times as much KE as the other.

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**Title: Analyzing Kinetic Energy in Iceboat Racing**

**Two Iceboats Race on a Frictionless Surface**

Imagine two iceboats racing across a frictionless, horizontal, frozen lake. One iceboat has a mass of \( m \), and the other has a mass of \( 2m \). Both start from rest, with an identical constant force \( F \) exerted by the wind on each. This scenario raises an intriguing question: which iceboat will cross the finish line with greater kinetic energy (KE)?

**Diagram Explanation:**

- The diagram depicts two iceboats racing from a start to a finish line over a distance \( s \).
- The blue iceboat is labeled with mass \( 2m \).
- The red iceboat is labeled with mass \( m \).
- Arrows denote the direction of the wind force \( F \) acting on both iceboats.

**Question:**

Which iceboat crosses the finish line with more kinetic energy?

**Options:**

1. The iceboat of mass \( 2m \): it has four times as much KE as the other.
2. The iceboat of mass \( m \): it has four times as much KE as the other.
3. The iceboat of mass \( 2m \): it has twice as much KE as the other.
4. **The iceboat of mass \( m \): it has twice as much KE as the other.** (Correct Answer)
5. They both cross the finish line with the same kinetic energy.

**Conclusion:**

When considering the kinetic energy differences, the iceboat of mass \( m \) ends the race with twice the kinetic energy of the iceboat with mass \( 2m \). This difference results from the relationship between force, mass, and acceleration, influencing the final velocities of the two iceboats.
Transcribed Image Text:**Title: Analyzing Kinetic Energy in Iceboat Racing** **Two Iceboats Race on a Frictionless Surface** Imagine two iceboats racing across a frictionless, horizontal, frozen lake. One iceboat has a mass of \( m \), and the other has a mass of \( 2m \). Both start from rest, with an identical constant force \( F \) exerted by the wind on each. This scenario raises an intriguing question: which iceboat will cross the finish line with greater kinetic energy (KE)? **Diagram Explanation:** - The diagram depicts two iceboats racing from a start to a finish line over a distance \( s \). - The blue iceboat is labeled with mass \( 2m \). - The red iceboat is labeled with mass \( m \). - Arrows denote the direction of the wind force \( F \) acting on both iceboats. **Question:** Which iceboat crosses the finish line with more kinetic energy? **Options:** 1. The iceboat of mass \( 2m \): it has four times as much KE as the other. 2. The iceboat of mass \( m \): it has four times as much KE as the other. 3. The iceboat of mass \( 2m \): it has twice as much KE as the other. 4. **The iceboat of mass \( m \): it has twice as much KE as the other.** (Correct Answer) 5. They both cross the finish line with the same kinetic energy. **Conclusion:** When considering the kinetic energy differences, the iceboat of mass \( m \) ends the race with twice the kinetic energy of the iceboat with mass \( 2m \). This difference results from the relationship between force, mass, and acceleration, influencing the final velocities of the two iceboats.
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