Passengers on the deck of a boat with a speed of Vs= 20⁡ m/s with the given direction experience a wind blowing at a speed of Vw = 10⁡ m/s as shown. What is the magnitude of the wind speed experienced by someone on the shore? ### Understanding Relative Motion in Boating with Wind Influence: An Educational OverviewThe image showcases a boat in motion on the water, illustrating concepts of relative motion influenced by wind.**Boat and Wind Vectors:**1. **Boat Velocity (\( v_s \))**: - The boat is moving with a velocity (\( v_s \)) of 20 meters per second. - The direction of the boat's motion is inclined 45 degrees from the horizontal axis. - This forms a right-angled triangle with its direction forming the hypotenuse at a 45-degree angle to the x-axis.2. **Wind Velocity (\( v_w \))**: - The wind is blowing towards the boat with a velocity (\( v_w \)) of 10 meters per second. - The direction of the wind is 30 degrees to the left of the vertical y-axis.**Coordinate Axes:**- The image provides a Cartesian coordinate system with the x-axis and y-axis intersecting at the right angle. - The boat’s motion forms a specific angle with these axes which helps in calculating the components of the quadratic velocities.By analyzing the vectors provided, students can gain deeper insights into how the motion of the boat is influenced by the wind. The trajectory and effective speed of the boat can be examined by breaking down these vectors into their horizontal (x) and vertical (y) components using trigonometric functions.### Mathematical Analysis:1. **Horizontal and Vertical Components**: - For the boat’s velocity \( v_s \): - Horizontal component (\( v_{sx} \)): \( v_s \cos(45^\circ) \) - Vertical component (\( v_{sy} \)): \( v_s \sin(45^\circ) \) - For the wind’s velocity \( v_w \): - Horizontal component (\( v_{wx} \)): \( v_w \cos(30^\circ) \) - Vertical component (\( v_{wy} \)): \( v_w \sin(30^\circ) \)2. **Resultant Velocities**: - By combining these components, the resultant velocity vectors can be determined, providing insight into the boat’s overall direction and speed under the influence of both its propulsion and wind.### Practical Application:This schematic representation allows students to understand and practice calculations involving relative velocity, trigonometry, and vector addition in physics, particularly in

Name: Passengers on the deck of a boat with a speed of Vs= 20⁡ m/s with the
Uploaded: 2024-03-20T06:57:47.000Z
Channel: Bartleby
Description: Passengers on the deck of a boat with a speed of Vs= 20⁡ m/s with the given direction experience a wind blowing at a speed of Vw = 10⁡ m/s as shown. What is the magnitude of the wind speed experienced by someone on the shore? ### Understanding Relati