Projectile Motion
Launch projectiles at various angles. Builds on 1D Kinematics.
A bullet is fired perfectly horizontally from the edge of a cliff. At the exact same instant, a ball is simply dropped from the same height.
Which one hits the ground first?
They hit the ground at the exact same time! Horizontal velocity has NO effect on vertical fall. Both experience the same gravitational acceleration downward. The bullet just lands much farther away.
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Watch the dropped ball and fired bullet fall together. Change the launch speed — they ALWAYS land simultaneously.
y = v₀sinθ·t − ½gt²
The magic angle is 45° — it maximizes range. But 30° and 60° give the SAME range! (sin2θ is the same for complementary angles.)
Pros kick at ~25° (not 45°) because they need to clear the wall AND keep the ball dipping. Air resistance changes the optimal angle.
Lava projectiles follow parabolic paths. Volcanologists use their landing positions to calculate eruption velocities.
Rifle scopes are calibrated for bullet drop — the bullet falls the entire time it's flying. A scope aimed 'dead on' would miss low at distance.
“A cannonball and a marble, dropped from the same height, hit the ground together. Galileo knew this. Newton explained why. Now you've seen it.”
Projectile Range
Launch projectiles at any angle and speed. Find the angle that gives maximum range.
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Fire at 30° and then at 60°. They land at the same distance! Now try 45° — the maximum range.
Complementary angles (like 30° and 60°) always give the same range. 45° is the sweet spot that maximizes distance.