Two constant forces are applied to a 100.0 kg boat, as shown in the diagram below. Assume that no other forces act in the x-y pane. Find the magnitude and direction of the boat's acceleration.

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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 Description:**

Two constant forces are applied to a 100.0 kg boat, as shown in the diagram below. Assume that no other forces act in the x-y plane. Find the magnitude and direction of the boat’s acceleration.

**Diagram Analysis:**

- The diagram shows a top view of a boat.
- Two forces are applied to the boat at different angles.
  
  - **Force 1:** 
    - Magnitude: 75.6 N
    - Direction: 30.9° from the positive x-axis, pointing upwards (red arrow).

  - **Force 2:** 
    - Magnitude: 87.2 N
    - Direction: 23.4° from the positive x-axis, pointing downwards (blue arrow).

- The coordinate system is defined with the x-axis pointing horizontally to the right and the y-axis pointing vertically up.

**Objective:**

Find the magnitude and direction of the resulting acceleration of the boat using the given forces and angles. Apply Newton’s second law of motion: \( F = ma \), where \( F \) is the net force on the object, \( m \) is the mass of the object, and \( a \) is the acceleration.
Transcribed Image Text:**Problem Description:** Two constant forces are applied to a 100.0 kg boat, as shown in the diagram below. Assume that no other forces act in the x-y plane. Find the magnitude and direction of the boat’s acceleration. **Diagram Analysis:** - The diagram shows a top view of a boat. - Two forces are applied to the boat at different angles. - **Force 1:** - Magnitude: 75.6 N - Direction: 30.9° from the positive x-axis, pointing upwards (red arrow). - **Force 2:** - Magnitude: 87.2 N - Direction: 23.4° from the positive x-axis, pointing downwards (blue arrow). - The coordinate system is defined with the x-axis pointing horizontally to the right and the y-axis pointing vertically up. **Objective:** Find the magnitude and direction of the resulting acceleration of the boat using the given forces and angles. Apply Newton’s second law of motion: \( F = ma \), where \( F \) is the net force on the object, \( m \) is the mass of the object, and \( a \) is the acceleration.
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