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Projectile Lab
Class XI · Kinematics: tune launch speed & angle.
Controls
Launch speed u30.0 m/s
Launch angle θ45 °
Gravity g9.8 m/s²
Initial height h₀0.0 m
Live readouts
Time of flight T4.33 s
Max height H22.96 m
Range R91.84 m
t (running)0.00 s
Formula
x(t) = u cosθ · t y(t) = h₀ + u sinθ · t − ½ g t² T = (u sinθ + √(u²sin²θ + 2g h₀)) / g H = h₀ + u²sin²θ / 2g R = u cosθ · T
Try this: Lock u = 30 m/s and sweep θ from 30° to 60°. Is the range really maximum at 45°? Now set h₀ = 20 m — does that still hold? (Hint: with h₀ > 0 the optimum drops below 45°.)