Someone on a skateboard is pulled by a rope attached to a bike. The velocity of the skateboarder is = (4.1 m/s) and the force exerted on her by the rope is = (17N)t + (12N))}. a) Find the work done on the skateboarder by the rope in 25 seconds. b) Determine the angle between the force and displacement. c) Assuming the velocity of the bike is the same as the skateboarder, find the work the rope does on the bike in 25 seconds. skateboard 177 bike

College Physics
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Problem Statement

Someone on a skateboard is pulled by a rope attached to a bike. The velocity of the skateboarder is \( \vec{v} = (4.1 \, \frac{\text{m}}{\text{s}}) \hat{\imath} \) and the force exerted on her by the rope is \( \vec{F} = (17 \, \text{N}) \hat{\imath} + (12 \, \text{N}) \hat{\jmath} \).

**Tasks:**

a) Find the work done on the skateboarder by the rope in 25 seconds.

b) Determine the angle between the force and displacement.

c) Assuming the velocity of the bike is the same as the skateboarder, find the work the rope does on the bike in 25 seconds.

### Diagram Explanation

The diagram accompanying the problem shows a representation of the forces and movement involved:

- **Skateboarder and Bike:** The skateboarder is on a straight path leading away from the bike.
- **Forces Indicated:**
  - A 17 N force vector pointing horizontally in the direction of motion (indicated by an arrow along the skateboarder’s path).
  - A 12 N force vector pointing vertically, forming a right angle with the horizontal force.
  - The resultant force \( \vec{F} \) at an angle \( \theta \) relative to the skateboarder's direction of motion.
- **Displacement Vector \( \vec{d} \):** Parallel to the velocity vector of the skateboarder, indicating the direction of movement.
  
This diagram helps in understanding the components of force and their relation to the skateboarder's motion.
Transcribed Image Text:### Problem Statement Someone on a skateboard is pulled by a rope attached to a bike. The velocity of the skateboarder is \( \vec{v} = (4.1 \, \frac{\text{m}}{\text{s}}) \hat{\imath} \) and the force exerted on her by the rope is \( \vec{F} = (17 \, \text{N}) \hat{\imath} + (12 \, \text{N}) \hat{\jmath} \). **Tasks:** a) Find the work done on the skateboarder by the rope in 25 seconds. b) Determine the angle between the force and displacement. c) Assuming the velocity of the bike is the same as the skateboarder, find the work the rope does on the bike in 25 seconds. ### Diagram Explanation The diagram accompanying the problem shows a representation of the forces and movement involved: - **Skateboarder and Bike:** The skateboarder is on a straight path leading away from the bike. - **Forces Indicated:** - A 17 N force vector pointing horizontally in the direction of motion (indicated by an arrow along the skateboarder’s path). - A 12 N force vector pointing vertically, forming a right angle with the horizontal force. - The resultant force \( \vec{F} \) at an angle \( \theta \) relative to the skateboarder's direction of motion. - **Displacement Vector \( \vec{d} \):** Parallel to the velocity vector of the skateboarder, indicating the direction of movement. This diagram helps in understanding the components of force and their relation to the skateboarder's motion.
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