What Is Projectile Motion?

Understanding the projectile motion is as easy as throwing a ball into the air. When the ball moves in air along with a curve that motion is what we call projectile motion. If you’re more into sports, you might have seen it before in the form of a soccer ball soaring towards a goal post or a basketball curving towards the net. It always involves a curved path that happens due to gravitational pull while the object is still moving. Quite easy, right? A projectile motion depends on three things:

• Initial speed: how fast the object is launched.
• Launch angle; how steeply it’s thrown.
• Gravity; that pulls it downward at 9.8 m/s².

How to Use the Projectile Motion Calculator?

What makes our Projectile Motion Calculator great is that you don't need to be a physics genius to navigate or use it. Here are a few simple steps that you can follow to calculate your projectile motion values:

Step 1: Enter Your Values

After navigating to our free Projectile Motion Calculator, you need to enter what you know. You can calculate trajectory, range, and time of flight by using our calculator. All you need to do is enter these value:

• Initial velocity in meters per second (m/s).
• Launch angle in degrees (°).
• Initial height in meters. If you don't know it can be zero.

Step 2: Press the "Calculate" Button

After entering all the known values, all you need to do is click the calculate button present at the bottom. You will get your results instantly.

Step 3: Check Your Results

Once pressed on the calculate button, you can find different results including total time the object stays in the air, maximum height it goes, in a horizontal range how far it travels and the final speed when it lands down.

How It Works – The Physics Behind the Magic

Science is supposed to be all magic due to physics, and even though it looks like simple magic when you use a calculator, it has its physics behind it. Our Projectile Motion Calculator uses physics equations to break motion into vertical and horizontal parts. It uses the following equations to calculate:

Time of Flight

Formula: t = (2 × v × sin(θ)) ÷ g

This is how long the object stays in the air.

Maximum Height

Formula: H = (v² × sin²(θ)) ÷ (2 × g)

This tells you how high the object travels before it starts coming down.

Horizontal Range

Formula: R = (v² × sin(2θ)) ÷ g

This is the total horizontal distance it covers. All results are based on a gravity value of 9.8 m/s².

Example

For Example: At an angle of 30 degrees above the horizontal, a ball is launched from the ground with an initial velocity of 20 m/s. Gravitational acceleration is 9.81 m/s², and there is no air resistance.

• Time of flight
• Maximum height
• Range
• Time to max height

Put 20 m/s in the initial velocity bar, 30° in the launch angle bar, and 0 in the initial height, and click on calculate.

Step-by-Step Solution

1. Step 1: Projectile Motion Analysis
2. Step 2: Initial velocity: 20 m/s at 30°
3. Step 3: Initial height: 0 m
4. Step 4: Velocity components:
5. Step 5: v₀ₓ = v₀cos(θ) = 20 × cos(30°) = 17.321 m/s
6. Step 6: v₀ᵧ = v₀sin(θ) = 20 × sin(30°) = 10 m/s
7. Step 7: Time to max height: t = v₀ᵧ/g = 10/9.81 = 1.019 s
8. Step 8: Maximum height: h = h₀ + v₀ᵧ²/(2g) = 0 + 5.097 = 5.097 m
9. Step 9: Time of flight: t = (v₀ᵧ + √(v₀ᵧ² + 2gh₀))/g = 2.039 s
10. Step 10: Range: R = v₀ₓ × t = 17.321 × 2.039 = 35.312 m

Result:

• Time of flight: 2.039 s
• Maximum height: 5.097 m
• Range: 35.312 m
• Time to max height: 1.019 s

Why Choose This Calculator?

There are thousands of students, teachers, and engineers who love using our calculators. There are many reasons for choosing our calculator as your physics partner, few of them are;

Fast & Error-Free

Get your results accurate by few clicks instead of solving lengthy equations by yourself.

Perfect for All Ages

From middle school to college goers, this calculator is perfect and tailored to your needs of physics projects and problems. It is easy to use and helps you to have a better understanding of your topics.

Free, Reliable & Online

You don't need to sign up, download or pay to use this calculator that makes it reliable and quick.

FAQS

Can I use this calculator to solve my college project related to projectile motion?

Yes, if your project has problems or you need to find time of flight, height or range, this calculator is perfect for you.

What should I know before using this calculator?

You need to add values with consistent units. You can check the unit mentioned in every requirement section of the calculator.

Is it free to use?

Yes, this calculator is free for everyone, with no hidden requirements.

Solve Your Physics Projects Quick, Free & Online With MathCalc

Learn More!