Solved Examples of 2D Projectile Trajectory Calculations

📚 Quick Study Guide

• 📏 [Relevant Emoji] Projectile motion is the motion of an object thrown or projected into the air, subject only to gravity and air resistance. We often ignore air resistance for simplified calculations.
• 🎯 [Relevant Emoji] The trajectory is a parabolic path.
• ➗ [Relevant Emoji] We analyze projectile motion by breaking it into horizontal and vertical components.
• ⏳ [Relevant Emoji] Time is the unifying variable between the horizontal and vertical motions.
• 📐 [Relevant Emoji] Initial velocity components are calculated as: $v_{0x} = v_0 \cos(\theta)$ and $v_{0y} = v_0 \sin(\theta)$, where $v_0$ is the initial velocity and $\theta$ is the launch angle.
• ➕ [Relevant Emoji] Horizontal motion: constant velocity, $x = x_0 + v_{0x}t$.
• ➖ [Relevant Emoji] Vertical motion: constant acceleration (due to gravity, $g = 9.8 m/s^2$), $y = y_0 + v_{0y}t - \frac{1}{2}gt^2$ and $v_y = v_{0y} - gt$.
• ⛰️ [Relevant Emoji] Maximum height is reached when $v_y = 0$.
• ✈️ [Relevant Emoji] Range is the horizontal distance traveled when the projectile returns to its initial height (if launched from and landing on the same level).

🧪 Practice Quiz

1. A ball is thrown horizontally with a speed of 10 m/s from the top of a 20 m high building. How far from the base of the building will the ball land?
   1. 5 m
   2. 10 m
   3. 20 m
   4. 20.2 m
2. A projectile is launched at an angle of 30° with an initial velocity of 30 m/s. What is the maximum height reached by the projectile?
   1. 11.48 m
   2. 22.96 m
   3. 45.92 m
   4. 9.8 m
3. A soccer ball is kicked with an initial velocity of 25 m/s at an angle of 45° above the horizontal. What is the range of the soccer ball?
   1. 31.89 m
   2. 63.78 m
   3. 127.55 m
   4. 255.1 m
4. An object is projected upwards with an initial velocity of 19.6 m/s. What is the time of flight?
   1. 1 s
   2. 2 s
   3. 3 s
   4. 4 s
5. A projectile is fired with an initial velocity of 50 m/s at an angle of 60° with the horizontal. What is the vertical component of the initial velocity?
   1. 25 m/s
   2. 43.3 m/s
   3. 50 m/s
   4. 28.87 m/s
6. If a projectile has a range of 80 m and is launched at an angle of 45°, what was its initial velocity?
   1. 14 m/s
   2. 28 m/s
   3. 32 m/s
   4. 40 m/s
7. What angle of projection results in the maximum range for a projectile launched from level ground, neglecting air resistance?
   1. 30°
   2. 45°
   3. 60°
   4. 90°