HomeConcept libraryPhysicsMechanicsMotion and Circular Motion

Concept module

Projectile Motion

Launch a projectile, watch the trajectory form, and connect the range, height, and component motion to the launch settings.

Interactive lab

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Featured setups

Earth shot

Open the balanced Earth launch with the trajectory and velocity vector visible.

Moon hop

Open the low-gravity launch and compare the stretched arc with the component graph.

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Stable links

Starter track

Step 2 of 30 / 3 complete

Motion and Circular Motion

Earlier steps still set up Projectile Motion.

1. Vectors and Components2. Projectile Motion3. Uniform Circular Motion

Previous step: Vectors and Components.

Start from track beginning

Why it behaves this way

Explanation

Projectile motion is what happens when an object gets an initial push and then gravity takes over. The horizontal and vertical parts of the motion separate cleanly, which makes the path predictable.

That separation is what makes the module useful. You can change launch speed, angle, and gravity, then watch the trajectory and its component graphs update together.

Key ideas

01The horizontal speed stays constant when drag is turned off.

02A 45 degree launch gives a long range only when the launch and landing heights match.

03Gravity changes the flight time and the arc, even if the launch speed stays fixed.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Solve the launch you are actually viewing. The givens and substitutions follow the real controls, and time-based examples follow the current inspected time unless you freeze them.

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Frozen valuesUsing frozen parameters

For the current launch settings, what horizontal range does the equal-height formula predict?

v_{0}

Launch speed

18 m/s

θ

Launch angle

45 °

g

Gravity

9.8 m/s²

1. Identify the relation

For equal launch and landing height, use

R = \frac{v _{0}^{2} sin ( 2 θ )}{g}

2. Substitute the current launch values

R = \frac{( 18 ) ^{2} sin ( 2 \cdot 4 5 ^{\circ} )}{9} .8

3. Compute the range

With

sin (2 θ) = 1

, the predicted range becomes

R = 33.06 m

Predicted range

R = 33.06 m

This angle keeps a fairly balanced split between horizontal reach and airtime, so the predicted range stays strong.

Common misconception

A steeper launch angle always gives a longer range.

Range depends on both horizontal and vertical components, not angle alone.

At the same launch speed, very steep angles waste horizontal speed and very shallow angles shorten flight time.

Mini challenge

If you keep speed fixed and lower the launch angle, what happens to the trajectory and the flight time?

Make a prediction before you reveal the next step.

Predict whether the arc gets taller or flatter.

Check your reasoning against the live bench.

The arc gets flatter and the flight time usually decreases.

A smaller angle sends more of the launch speed sideways and less upward, so gravity brings the object back down sooner.

Quick test

Compare cases

Question 1 of 4

Use the trajectory, the component graphs, and the launch variables together. Each question is meant to check whether you can explain the motion, not just name a formula.

At the same launch speed with equal launch and landing height, how do $3 0^{\circ}$ and $6 0^{\circ}$ launches compare?

Use the live bench to test the result before moving on.

Accessibility

The simulation shows a projectile launched from a point on the ground and traced through the air by gravity alone. The vector overlays can show the current velocity and its horizontal and vertical pieces.

Changing speed, launch angle, or gravity immediately reshapes the flight path, the landing point, and the component graphs.

Graph summary

The trajectory graph shows the curved flight path from launch to landing.

The component graphs show that horizontal motion stays steady while vertical motion bends under gravity.

Keep this idea moving

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Launch impulse viewMechanics

Projectile Motion

Motion and Circular Motion

Explanation

Step through the frozen example

For the current launch settings, what horizontal range does the equal-height formula predict?

At the same launch speed with equal launch and landing height, how do $3 0^{\circ}$ and $6 0^{\circ}$ launches compare?

Keep this idea moving

Momentum and Impulse

Vectors and Components

Gravitational Fields

Projectile Motion

Motion and Circular Motion

Explanation

Step through the frozen example

For the current launch settings, what horizontal range does the equal-height formula predict?

At the same launch speed with equal launch and landing height, how do 30∘ and 60∘ launches compare?

Keep this idea moving

Momentum and Impulse

Vectors and Components

Gravitational Fields

At the same launch speed with equal launch and landing height, how do $3 0^{\circ}$ and $6 0^{\circ}$ launches compare?