Physic Labs

Newtonian mechanics

Projectile motion

Study horizontal and oblique projectile motion under gravity. Verify the parabolic trajectory x=v0cos⁡θ⋅tx = v_0\cos\theta\cdot t, y=y0+v0sin⁡θ⋅t−12gt2y = y_0 + v_0\sin\theta\cdot t - \frac{1}{2}gt^2 and the independence of the two motion components.

High school

Equipment

  • 3D projectile model with trajectory drawn on canvas
  • Time slider to stop the trajectory at any instant
  • Parameter slider (launch speed/angle)
  • Velocity-component graphs and a Pause button

Procedure

  1. Read the parabolic trajectory

    Run the simulation and drag the time slider: the trajectory trace is a parabola symmetric about its apex (for oblique launch). Read the apex coordinates on the canvas and compare with tmax⁡=v0sin⁡θ/gt_{\max} = v_0\sin\theta/g, ymax⁡=y0+(v0sin⁡θ)2/2gy_{\max} = y_0 + (v_0\sin\theta)^2/2g.

  2. Split into horizontal and vertical parts

    Use Pause at several instants: the horizontal velocity vxv_x stays constant on the plot while vyv_y decreases linearly as vy=v0sin⁡θ−gtv_y = v_0\sin\theta - gt. Measure horizontal distances over equal time intervals to see uniform horizontal motion.

  3. Change the parameter and predict range

    Drag the parameter slider to change launch speed or angle and watch the range. For ground-level oblique launch, R=v02sin⁡2θ/gR = v_0^2\sin 2\theta/g: predict which angle gives maximum range before checking, and note that complementary angles give equal ranges.

Simulation

Experiment history

The Aristotelian claim that heavy bodies fall faster persisted for two thousand years. In 1604 Galileo Galilei demonstrated objects fall with constant acceleration and, analyzing horizontally shot projectiles in the Discorsi (1638), concluded the trajectory is a parabola — the result of independent uniform horizontal motion and accelerated vertical fall. The notion of "inertia" preserving horizontal motion grew from Galileo's inclined-plane and groove experiments; Newton formalized it as the first law in the Principia (1687). Galileo's superposition principle for motions underlies all modern ballistics.

Related physicists

Galileo GalileiIsaac Newton

Related library topics

Projectile motion