Every attempt at this target is drawn (green = hit, grey = miss). The red mark is the target.
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Target
h / m
u / m s⁻¹
θ / °
Miss / m
Result
Help
How to use this simulation
Choose a target: a cup on the floor, a basketball hoop or a window in a wall. Set its distanceD and
height, or press 🎯 New target for a random one.
Set each value with ▼ and ▲ (hold to go faster; the ↑ ↓ keys or the mouse wheel in the box also work, Shift = ×10), or type a value in the box. ↺ puts it back to its start value. Outside the classroom range the box turns amber ⚠: fine to explore, but the lab can't do this.
Move the pointer over any graph (or tap it): a dashed line shows the values where it cuts each curve, or the values of the nearest data point.
Set the launch speedu, angleθ (0° = horizontal, negative = downward) and launch heighth.
Use the shot planner (middle column): it does the working for your settings — time to reach the target distance,
then the height of the ball there. Change u or θ until the ball arrives at the target height.
Press ▶ Shoot. A cup or hoop counts only if the ball comes down into it; a window counts if the ball passes through it.
◂ 0.1 s / 0.1 s ▸ (or the ← → keys) step the motion back and forward and pause it, so you can discuss
each moment: the velocity and acceleration arrows stay on the screen. Graph tools: Area shades the area under
a velocity graph (= displacement) or an acceleration graph (= change in velocity) up to that moment and writes what the area is (its name and value) inside it; Tangent draws the
tangent there (gradient of a position graph = velocity, of a velocity graph = acceleration).
The Attempts tab plots your attempts on a u–θ graph with the needed-speed curve: every point on the curve hits.
The physics
Horizontal: t = D / (u cos θ) — the time to reach the target distance.
Vertical: y = h + u sin θ · t − ½gt² — the height of the ball at that time.
Together: y = h + D tan θ − gD² / (2u² cos² θ). Set y equal to the target height and solve for
u (one answer) or for θ (usually two answers: a low and a high shot).
Model: no air resistance; g = 9.81 m s⁻². Cup width 0.30 m, hoop width 0.46 m, window height 0.80 m.
Newton's laws
The badge above the scene says which law applies at this moment: 1st law — at rest or moving at a constant velocity, the resultant force is zero (ΣF = 0); 2nd law — accelerating, ΣF = ma. The table under the free-body diagram adds up the forces (ΣF) and compares them with m a (▾ folds it). Tick 3rd-law pairs to see every force with its partner: the same size and type, in the opposite direction, acting on the other body (the Earth, the floor, the string, the fluid…).