Motion and Projectile Simulator

Fire a projectile and change its speed, angle and launch height, or try other planets. Switch to Motion graphs to see how position, velocity and acceleration are linked for a moving car or a falling stone. Then test yourself with predict-and-check problems.

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Equations of motion

Constant acceleration in a straight line

v = u + at

s = ut + ½at² = (u + v)t / 2

v² = u² + 2as

On a velocity-time graph the slope is the acceleration and the area under the line is the displacement. On a position-time graph the slope is the velocity.

Projectile motion

Split the launch velocity: v_x = v cosθ and v_y = v sinθ.

Horizontally there is no acceleration, so v_x is constant. Vertically the acceleration is g downwards.

From the ground: T = 2v sinθ / g, H = v² sin²θ / 2g, R = v² sin 2θ / g.

The range is greatest at 45°, and angles that add up to 90° give the same range.

Things to try

Set the height to 0 and compare 30° and 60°: same range, different heights and times. Turn on Keep earlier paths to see them together.
Launch horizontally (0°) from a height and tick Drop a second ball. Both hit the ground at the same instant: horizontal motion does not change how fast something falls.
Choose the Moon and fire the same shot. The range is about six times longer because g is about six times smaller.
Turn on air resistance and find the new best angle.
Use Target practice: there are always two angles that reach the target.

Practise what you learned

Test yourself with chapter-wise MCQs and explanations:

Forces and Motion — Physics, HSSC-KPK First Year (930 questions)
Rotational and Circular Motion — Physics, HSSC-KPK First Year (740 questions)
Fluid Dynamics — Physics, HSSC-KPK First Year (672 questions)
Thermodynamics — Physics, HSSC-KPK First Year (975 questions)
Force and Motion — Physics, HSSC-Punjab First Year (1,275 questions)
Circular and Rotational Motion — Physics, HSSC-Punjab First Year (802 questions)
Solids and Fluid Dynamics — Physics, HSSC-Punjab First Year (1,260 questions)
Heat and Thermodynamics — Physics, HSSC-Punjab First Year (943 questions)
Simple Harmonic Motion — Physics, HSSC-Punjab Second Year (1,217 questions)
Kinematics — Physics, SSC-KPK Class 9 (636 questions)
Dynamics — Physics, SSC-KPK Class 9 (653 questions)
Turning Effect of Forces — Physics, SSC-KPK Class 9 (394 questions)
Simple Harmonic Motion and Waves — Physics, SSC-KPK Class 10 (1,145 questions)
Kinematics — Physics, SSC-Punjab Class 9 (1,120 questions)
Dynamics — Physics, SSC-Punjab Class 9 (1,220 questions)
Turning Effects of Forces — Physics, SSC-Punjab Class 9 (1,016 questions)

Without air resistance the exact formulas are used. With air resistance the drag is taken as proportional to the square of the speed and the path is calculated step by step. Works offline: after your first visit the simulator is saved in your browser.