Solved Examples: Calculating Terminal Velocity with Air Resistance

📚 Quick Study Guide

• 🍎 Terminal Velocity Defined: Terminal velocity is the constant speed that a freely falling object eventually reaches when the force of air resistance equals the force of gravity.
• ⚖️ Forces Involved: At terminal velocity, the net force on the object is zero ($F_{net} = 0$), meaning the gravitational force ($F_g$) equals the drag force ($F_d$).
• 💨 Drag Force: The drag force due to air resistance is often modeled as $F_d = \frac{1}{2} \rho v^2 C_d A$, where $\rho$ is the air density, $v$ is the velocity, $C_d$ is the drag coefficient, and $A$ is the cross-sectional area.
• 📏 Calculating Terminal Velocity: To find the terminal velocity ($v_t$), set $F_g = F_d$, so $mg = \frac{1}{2} \rho v_t^2 C_d A$. Solve for $v_t$ to get $v_t = \sqrt{\frac{2mg}{\rho C_d A}}$.
• 💡 Factors Affecting Terminal Velocity: Mass ($m$), air density ($\rho$), drag coefficient ($C_d$), and cross-sectional area ($A$) all influence terminal velocity.

🧪 Practice Quiz

1. What is terminal velocity?
   1. The velocity of an object when it hits the ground.
   2. The constant speed reached when air resistance equals gravity.
   3. The maximum velocity an object can achieve in a vacuum.
   4. The initial velocity of a falling object.
2. Which of the following forces are equal at terminal velocity?
   1. Applied force and normal force.
   2. Tension and weight.
   3. Gravity and air resistance.
   4. Friction and gravity.
3. What happens to the net force on an object when it reaches terminal velocity?
   1. It increases.
   2. It decreases.
   3. It remains constant but non-zero.
   4. It becomes zero.
4. An object with a larger cross-sectional area will generally have:
   1. A higher terminal velocity.
   2. A lower terminal velocity.
   3. The same terminal velocity as a smaller object.
   4. No terminal velocity.
5. If the mass of an object increases, what happens to its terminal velocity?
   1. It increases.
   2. It decreases.
   3. It remains the same.
   4. It becomes zero.
6. Which of the following factors does NOT directly affect terminal velocity?
   1. The object's mass.
   2. The air density.
   3. The object's initial velocity.
   4. The object's cross-sectional area.
7. A skydiver opens their parachute. What happens to their terminal velocity?
   1. It increases.
   2. It decreases.
   3. It remains the same.
   4. It becomes infinite.