What is Terminal Velocity?

S6-SA3-0293

Grade Level:

Class 10

AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine

Definition

What is it?

Terminal velocity is the constant speed that a free-falling object eventually reaches when the resistance of the medium through which it is falling (like air) prevents further acceleration. It happens when the downward force of gravity equals the upward force of air resistance.

Simple Example

Quick Example

Imagine a cricket ball dropped from a very high building. Initially, it speeds up due to gravity. But as it falls faster, the air pushes back more strongly. Eventually, the upward air resistance will become equal to the downward pull of gravity, and the ball will stop speeding up, continuing to fall at a constant maximum speed – this is its terminal velocity.

Worked Example

Step-by-Step

Let's find the terminal velocity for a small raindrop (mass = 0.000001 kg, air resistance constant k = 0.0000001 Ns/m). We know that at terminal velocity, gravitational force equals air resistance. Gravitational force (Fg) = mass (m) * acceleration due to gravity (g). Air resistance (Fr) = k * velocity (v). --- Step 1: Write down the forces. Fg = m * g. Fr = k * v. --- Step 2: Set forces equal at terminal velocity (Vt). m * g = k * Vt. --- Step 3: Rearrange to solve for Vt. Vt = (m * g) / k. --- Step 4: Plug in the values. g is approximately 9.8 m/s^2. Vt = (0.000001 kg * 9.8 m/s^2) / 0.0000001 Ns/m. --- Step 5: Calculate the value. Vt = 0.0000098 / 0.0000001. --- Step 6: Simplify. Vt = 98 m/s. --- Answer: The terminal velocity of the raindrop is 98 m/s.

Why It Matters

Understanding terminal velocity is crucial in designing parachutes for safe landings in space missions (ISRO uses this!), creating aerodynamic cars and planes, and even in biotechnology for separating particles. It helps engineers build safer vehicles and helps scientists understand how things move through fluids.

Common Mistakes

MISTAKE: Thinking that an object stops falling once it reaches terminal velocity. | CORRECTION: An object continues to fall at a constant speed, it just stops accelerating.

MISTAKE: Believing that all objects fall at the same terminal velocity. | CORRECTION: Terminal velocity depends on an object's mass, shape, and surface area, so different objects have different terminal velocities.

MISTAKE: Confusing terminal velocity with initial speed or free fall acceleration. | CORRECTION: Terminal velocity is a constant speed reached when air resistance balances gravity, not the initial speed or the acceleration (which becomes zero at terminal velocity).

Practice Questions

Try It Yourself

QUESTION: Why does a feather fall slower than a stone of the same weight when dropped from the same height? | ANSWER: A feather has a larger surface area relative to its weight, so it experiences more air resistance at lower speeds, reaching its (much lower) terminal velocity faster than the stone.

QUESTION: A skydiver jumps from a plane. Describe the forces acting on her just before she opens her parachute, assuming she has reached terminal velocity. | ANSWER: Just before opening her parachute at terminal velocity, the downward force of gravity (her weight) is exactly balanced by the upward force of air resistance.

QUESTION: If a 70 kg skydiver has a terminal velocity of 50 m/s before opening their parachute, what is the air resistance acting on them at that moment? (Assume g = 10 m/s^2) | ANSWER: At terminal velocity, air resistance equals gravitational force. Gravitational force = mass * g = 70 kg * 10 m/s^2 = 700 N. So, air resistance is 700 N.

MCQ

Quick Quiz

What happens to the acceleration of an object once it reaches terminal velocity?

It increases rapidly

It becomes zero

It stays constant but non-zero

It decreases but never reaches zero

The Correct Answer Is:

At terminal velocity, the net force on the object is zero because gravity is balanced by air resistance. According to Newton's second law (F=ma), if the net force is zero, the acceleration must also be zero.

Real World Connection

In the Real World

When you see delivery drones like those used by startups in India delivering packages, their descent rate is carefully controlled. Engineers use the principles of terminal velocity to design these drones so they can descend safely and gently, ensuring the package doesn't get damaged upon landing, rather than free-falling.

Key Vocabulary

Key Terms

GRAVITY: The force that pulls objects towards the center of the Earth. | AIR RESISTANCE: The force that opposes the motion of an object through the air. | ACCELERATION: The rate at which an object's velocity changes. | FREE FALL: The motion of an object solely under the influence of gravity.

What's Next

What to Learn Next

Great job understanding terminal velocity! Next, explore Newton's Laws of Motion. They will help you understand the fundamental principles behind why objects move (or stop accelerating) the way they do, building on what you've learned about forces and motion.