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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I need help with question 8
![**Problem 8: Projectile Motion**
You want to land a projectile 1 meter away from where it is launched at a speed of 4.4 meters per second. What angles can be used?
**Explanation:**
This problem involves determining the launch angles required to land a projectile exactly 1 meter away, given a launch speed of 4.4 m/s. The solution involves applying principles of projectile motion, specifically calculating the range of a projectile using its initial velocity and launch angle.
To solve the problem:
1. **Use the range formula for projectile motion**, which is given by:
\[
R = \frac{v^2 \sin(2\theta)}{g}
\]
Where:
- \( R \) is the range (1 meter in this problem),
- \( v \) is the initial velocity (4.4 m/s),
- \( \theta \) is the launch angle,
- \( g \) is the acceleration due to gravity (approximately 9.81 m/s\(^2\)).
2. **Solve for the angle \(\theta\)**, knowing that the range \( R \) should equal 1 meter.
By substituting the known values into the range equation, students can solve for the angle(s) \(\theta\) that will result in the projectile traveling exactly 1 meter. Graphics or diagrams depicting the trajectory of the projectile would show the initial velocity vector, the height and range, and how varying \(\theta\) changes the path.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c1ac660-1734-4e58-bb08-c8b54c6e23fd%2Ff73c28a1-20fe-4949-883c-e98e970ea794%2Fq9r30c5_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 8: Projectile Motion**
You want to land a projectile 1 meter away from where it is launched at a speed of 4.4 meters per second. What angles can be used?
**Explanation:**
This problem involves determining the launch angles required to land a projectile exactly 1 meter away, given a launch speed of 4.4 m/s. The solution involves applying principles of projectile motion, specifically calculating the range of a projectile using its initial velocity and launch angle.
To solve the problem:
1. **Use the range formula for projectile motion**, which is given by:
\[
R = \frac{v^2 \sin(2\theta)}{g}
\]
Where:
- \( R \) is the range (1 meter in this problem),
- \( v \) is the initial velocity (4.4 m/s),
- \( \theta \) is the launch angle,
- \( g \) is the acceleration due to gravity (approximately 9.81 m/s\(^2\)).
2. **Solve for the angle \(\theta\)**, knowing that the range \( R \) should equal 1 meter.
By substituting the known values into the range equation, students can solve for the angle(s) \(\theta\) that will result in the projectile traveling exactly 1 meter. Graphics or diagrams depicting the trajectory of the projectile would show the initial velocity vector, the height and range, and how varying \(\theta\) changes the path.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Motion of projectile can be divided into x component and y component.
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Solved in 2 steps with 1 images
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