**Physics Problem: Calculating the Magnitude of Final Velocity****Problem Statement:**You threw a tennis ball from a balcony 4.1 meters above the ground upward at an angle of 45 degrees above horizontal with an initial speed of 4.0 meters per second. What was the magnitude of the total final velocity?**Detailed Breakdown:**1. **Initial Conditions:** - Height of the balcony: 4.1 meters above the ground - Launch angle: 45 degrees above the horizontal - Initial speed: 4.0 meters per second2. **Calculating the Initial Velocity Components:** - Horizontal component (\(v_{0x}\)): \(v_{0x} = v_0 \cdot \cos(\theta)\) \[ v_{0x} = 4.0 \, \text{m/s} \cdot \cos(45^\circ) = 4.0 \, \text{m/s} \cdot \frac{\sqrt{2}}{2} = 2.83 \, \text{m/s} \] - Vertical component (\(v_{0y}\)): \(v_{0y} = v_0 \cdot \sin(\theta)\) \[ v_{0y} = 4.0 \, \text{m/s} \cdot \sin(45^\circ) = 4.0 \, \text{m/s} \cdot \frac{\sqrt{2}}{2} = 2.83 \, \text{m/s} \]3. **Vertical Motion Analysis:** - Use the kinematic equation for vertical motion: \[ y = v_{0y}t + \frac{1}{2} a t^2 \] where \( y \) is the displacement (4.1 m), \( v_{0y} \) is the initial vertical velocity (2.83 m/s), \( a \) is the acceleration due to gravity (-9.8 m/s²), and \( t \) is the time of flight. 4. **Solving for Time of Flight:** - Solving the quadratic equation: \[ 4.1 = 2.83t - \frac{1}{2}(9.8)t^

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Description: **Physics Problem: Calculating the Magnitude of Final Velocity****Problem Statement:**You threw a tennis ball from a balcony 4.1 meters above the ground upward at an angle of 45 degrees above horizontal with an initial speed of 4.0 meters per second

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You threw a tennis ball from a balcony 4.1 m above the ground upward at 45 degrees above horizontal with an initial speed of 4.0 m/s. What was the magnitude of the total final velocity?

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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