College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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An object is launched at a velocity of 25 m/s in a direction making an angle of 20° upward with the horizontal.
What is the maximum height reached by the object?
- What is the horizontal range (maximum x above ground) of the object?
![### PHY 150 PROBLEM SET 3
#### Projectile Motion Equations
1. **Horizontal Velocity:**
\[ v_x = v_o \cos \theta = \text{constant} \]
2. **Vertical Velocity:**
\[ v_y = v_o \sin \theta \]
3. **Vertical Velocity at some time \( t \):**
\[ v_y = v_o (\sin \theta) - gt \]
where \( g = 9.8 \frac{m}{s^2} \)
4. **Vertical Velocity at height \( y \):**
\[ v_y^2 = (v_o \sin \theta)^2 - 2g \Delta y \]
5. **Horizontal Distance Traveled:**
\[ \Delta x = v_o (\cos \theta) t \]
6. **Vertical Distance Traveled:**
\[ \Delta y = (v_o \sin \theta)t - \frac{1}{2}gt^2 \]
7. **Time to Highest Point:**
\[ t = \frac{v_o \sin \theta}{g} \]
8. **Total Flight Time:**
\[ t = \frac{2v_o \sin \theta}{g} \]
These equations are fundamental in understanding the principles of projectile motion. They cover various aspects of projectile trajectory including horizontal and vertical components of velocity, displacement, and time calculations.
* **Horizontal Velocity ( \( v_x \) ):** This remains constant throughout the projectile’s flight.
* **Vertical Velocity ( \( v_y \) ):** This changes due to the influence of gravity.
* **Vertical Velocity at some time \( t \):** This is the initial vertical velocity minus the product of gravitational acceleration ( \( g \) ) and time ( \( t \) ).
* **Vertical Velocity at height \( y \):** This relation uses the squared initial vertical velocity, gravitational acceleration, and the vertical distance \( \Delta y \).
* **Horizontal Distance Traveled ( \( \Delta x \) ):** The distance covered horizontally over time.
* **Vertical Distance Traveled ( \( \Delta y \) ):** The distance covered vertically over time, adjusted for gravitational effects.
* **Time to Highest Point:** The time it takes for the projectile to reach its maximum height.
* **Total Flight Time:** The total duration the projectile is in](https://content.bartleby.com/qna-images/question/3f244e86-5051-4021-9cc0-b5054f2c0b68/22ef8280-478f-4ab5-a6c5-000b0371fa0b/oz1kokg_processed.jpeg)
Transcribed Image Text:### PHY 150 PROBLEM SET 3
#### Projectile Motion Equations
1. **Horizontal Velocity:**
\[ v_x = v_o \cos \theta = \text{constant} \]
2. **Vertical Velocity:**
\[ v_y = v_o \sin \theta \]
3. **Vertical Velocity at some time \( t \):**
\[ v_y = v_o (\sin \theta) - gt \]
where \( g = 9.8 \frac{m}{s^2} \)
4. **Vertical Velocity at height \( y \):**
\[ v_y^2 = (v_o \sin \theta)^2 - 2g \Delta y \]
5. **Horizontal Distance Traveled:**
\[ \Delta x = v_o (\cos \theta) t \]
6. **Vertical Distance Traveled:**
\[ \Delta y = (v_o \sin \theta)t - \frac{1}{2}gt^2 \]
7. **Time to Highest Point:**
\[ t = \frac{v_o \sin \theta}{g} \]
8. **Total Flight Time:**
\[ t = \frac{2v_o \sin \theta}{g} \]
These equations are fundamental in understanding the principles of projectile motion. They cover various aspects of projectile trajectory including horizontal and vertical components of velocity, displacement, and time calculations.
* **Horizontal Velocity ( \( v_x \) ):** This remains constant throughout the projectile’s flight.
* **Vertical Velocity ( \( v_y \) ):** This changes due to the influence of gravity.
* **Vertical Velocity at some time \( t \):** This is the initial vertical velocity minus the product of gravitational acceleration ( \( g \) ) and time ( \( t \) ).
* **Vertical Velocity at height \( y \):** This relation uses the squared initial vertical velocity, gravitational acceleration, and the vertical distance \( \Delta y \).
* **Horizontal Distance Traveled ( \( \Delta x \) ):** The distance covered horizontally over time.
* **Vertical Distance Traveled ( \( \Delta y \) ):** The distance covered vertically over time, adjusted for gravitational effects.
* **Time to Highest Point:** The time it takes for the projectile to reach its maximum height.
* **Total Flight Time:** The total duration the projectile is in
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