Solved Examples of Maximum Height in Projectile Motion

📚 Quick Study Guide

• 📐 Projectile motion involves an object thrown into the air, influenced only by gravity.
• ⬆️ Maximum height ($H$) is the highest vertical position the projectile reaches.
• Initial velocity ($v_0$) is the velocity at which the object is launched.
• Launch angle ($\theta$) is the angle between the initial velocity vector and the horizontal.
• The vertical component of initial velocity is $v_{0y} = v_0 \sin(\theta)$.
• At maximum height, the vertical velocity ($v_y$) is zero.
• The formula to calculate maximum height ($H$) is: $H = \frac{v_{0y}^2}{2g} = \frac{(v_0 \sin(\theta))^2}{2g}$, where $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$).
• ⏱️ Time to reach maximum height: $t = \frac{v_0 \sin(\theta)}{g}$

🧪 Practice Quiz

1. A projectile is launched with an initial velocity of 30 m/s at an angle of 60° with respect to the horizontal. What is the maximum height reached by the projectile? (Assume g = 9.8 m/s²)
   1. 17.2 m
   2. 34.4 m
   3. 22.9 m
   4. 45.8 m
2. A ball is thrown upward with an initial velocity of 20 m/s at an angle of 45°. Calculate the maximum height the ball attains. (Assume g = 9.8 m/s²)
   1. 10.2 m
   2. 20.4 m
   3. 14.3 m
   4. 28.6 m
3. An object is projected with an initial velocity of 40 m/s at an angle of 30° above the horizontal. Determine the maximum height reached by the object. (Assume g = 9.8 m/s²)
   1. 20.4 m
   2. 40.8 m
   3. 15.3 m
   4. 30.6 m
4. If a projectile reaches a maximum height of 25 meters when launched at an angle of 40°, what was its initial velocity? (Assume g = 9.8 m/s²)
   1. 20.0 m/s
   2. 28.0 m/s
   3. 14.0 m/s
   4. 36.0 m/s
5. A projectile is fired at an angle of 55° and reaches a maximum height of 30 meters. What is the initial velocity of the projectile? (Assume g = 9.8 m/s²)
   1. 28.2 m/s
   2. 19.8 m/s
   3. 14.1 m/s
   4. 36.4 m/s
6. A projectile launched at 60° reaches what maximum height if its initial velocity is 25 m/s? (Assume g = 9.8 m/s²)
   1. 22.9 m
   2. 19.1 m
   3. 15.3 m
   4. 26.7 m
7. What is the maximum height achieved by a projectile launched with an initial velocity of 35 m/s at an angle of 45°? (Assume g = 9.8 m/s²)
   1. 31.25 m
   2. 62.5 m
   3. 24.7 m
   4. 49.4 m