How to play Two Shadows
- Choose a throw and read the launch speed v₀ and the angle θ on the card.
- Split v₀ into vₓ = v₀·cos θ and v_y0 = v₀·sin θ.
- Treat the floor shadow as uniform motion at vₓ and the wall shadow as a vertical throw at v_y0. Type your answer.
- Press Play and watch both shadows. Turn on the strobe to compare their spacing.
A projectile is two motions at once
Light from straight above casts the ball's shadow on the floor; light from the side casts it on a wall. The floor shadow shows only the horizontal motion: with no horizontal force, it moves at the constant speed vₓ = v₀·cos θ, as in MRU. The wall shadow shows only the vertical motion: it starts up at v_y0 = v₀·sin θ, slows down, stops at the top, and falls back, exactly like a ball thrown straight up. A projectile is these two simple motions happening together, sharing the same clock t.
A focused learning model
The ball is a point launched from floor level with g = 9.8 m/s² and no air resistance, so its horizontal velocity never changes. The top and the landing are solved exactly at t = v_y0 ÷ g and t = 2·v_y0 ÷ g, and the velocity just before landing is kept. Every throw uses the same view, with one scale for both axes, and plays in real time.