### Projectile Motion Analysis **Problem Statement:** A projectile is launched at 20 m/s at an angle of 60 degrees. 1. Where is the projectile located at 2 seconds? 2. What are the maximum height attained and range for the projectile? **Calculations:** - **Max Height** = - **Range** = - **Location at 2 seconds** = ### Explanation: To solve these problems, we need to use the equations of motion for projectiles: 1. **Max Height**: This can be calculated using the formula: \[ h = \frac{(v_i^2 \cdot \sin^2(\theta))}{2g} \] where \( v_i \) is the initial velocity, \(\theta\) is the angle of projection, and \( g \) is the acceleration due to gravity (approximately 9.81 m/s²). 2. **Range**: The horizontal distance traveled by the projectile can be found using: \[ R = \frac{(v_i^2 \cdot \sin(2\theta))}{g} \] 3. **Location at 2 seconds**: The position of the projectile at a given time \( t \) can be found using: \[ x = v_i \cdot \cos(\theta) \cdot t \] \[ y = v_i \cdot \sin(\theta) \cdot t - \frac{1}{2} \cdot g \cdot t^2 \] By substituting the known values into these equations, the exact numerical answers can be obtained.

### Projectile Motion Analysis Problem Statement: A projectile is launched at 20 m/s at an angle of 60 degrees. 1. Where is the projectile located at 2 seconds? 2. What are the maximum height attained and range for the projectile? Calculations: - Max Height = - Range = - Location at 2 seconds = ### Explanation: To solve these problems, we need to use the equations of motion for projectiles: 1. Max Height: This can be calculated using the formula: \[ h = \frac{(v_i^2 \cdot \sin^2(\theta))}{2g} \] where \( v_i \) is the initial velocity, \(\theta\) is the angle of projection, and \( g \) is the acceleration due to gravity (approximately 9.81 m/s²). 2. Range: The horizontal distance traveled by the projectile can be found using: \[ R = \frac{(v_i^2 \cdot \sin(2\theta))}{g} \] 3. Location at 2 seconds: The position of the projectile at a given time \( t \) can be found using: \[ x = v_i \cdot \cos(\theta) \cdot t \] \[ y = v_i \cdot \sin(\theta) \cdot t - \frac{1}{2} \cdot g \cdot t^2 \] By substituting the known values into these equations, the exact numerical answers can be obtained.

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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