projectile motion examples with solutions

📚 Quick Study Guide

• 📐 Projectile motion is the motion of an object thrown or projected into the air, subject only to gravity.
• 🍎 The path the object follows is called its trajectory, which is parabolic.
• ⏱️ Key formulas include:
  • Initial velocity components: $v_{0x} = v_0 \cos(\theta)$, $v_{0y} = v_0 \sin(\theta)$
  • Horizontal displacement: $x = v_{0x} t$
  • Vertical displacement: $y = v_{0y} t - \frac{1}{2} g t^2$
  • Time of flight: $T = \frac{2 v_{0y}}{g}$
  • Maximum height: $H = \frac{v_{0y}^2}{2g}$
  • Range: $R = \frac{v_0^2 \sin(2\theta)}{g}$
  Where $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$).
• 💡 Remember to consider air resistance in real-world scenarios, though many introductory problems ignore it for simplicity.

🧪 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. 20.2 m
   4. 40.4 m
2. A projectile is launched at an angle of 30 degrees to the horizontal with an initial speed of 30 m/s. What is the maximum height reached by the projectile? (Assume g = 9.8 m/s²)
   1. 11.48 m
   2. 22.96 m
   3. 34.44 m
   4. 45.92 m
3. A stone is thrown upwards at an angle of 45 degrees with an initial velocity $v_0$. What is the ratio of its kinetic energy at the beginning to its kinetic energy at the highest point?
   1. 1:1
   2. 2:1
   3. 1:2
   4. $\sqrt{2}:1$
4. A soccer ball is kicked with an initial velocity of 25 m/s at an angle of 37 degrees above the horizontal. What is the total time the ball is in the air?
   1. 1.53 s
   2. 3.06 s
   3. 4.59 s
   4. 6.12 s
5. A projectile is fired with an initial velocity of $v$ at an angle of $\theta$ with the horizontal. What angle of projection will result in the maximum range?
   1. 30 degrees
   2. 45 degrees
   3. 60 degrees
   4. 90 degrees
6. Two projectiles are thrown with the same initial speed. Projectile A is launched at an angle of 30 degrees, and Projectile B is launched at an angle of 60 degrees. Which projectile will have a greater range (assuming level ground and no air resistance)?
   1. Projectile A
   2. Projectile B
   3. Both will have the same range
   4. Cannot be determined
7. A ball is dropped from a height of 100 m. At the same instant, another ball is thrown upwards from the ground with a velocity of 25 m/s. After what time will they meet? (Assume g = 9.8 m/s²)
   1. 2 s
   2. 4 s
   3. 6 s
   4. 8 s