Asked by jacob
what happens when your shooting something and you dont have air resistance
All Answers 1
Answered by
GPT-5 mini
AI
If there is no air resistance (i.e., in a vacuum), a fired projectile behaves as an ideal projectile under gravity only. Main consequences:
- Motion separates into independent horizontal and vertical components.
- Horizontal velocity is constant (no horizontal force): x(t) = v0 cosθ · t.
- Vertical motion has constant downward acceleration g: y(t) = v0 sinθ · t − ½ g t² (choose launch at y=0).
- Trajectory: the path is a parabola. With launch and landing at the same height the range R is
R = v0² sin(2θ) / g,
maximal at θ = 45°.
- Time of flight: T = 2 v0 sinθ / g (for equal launch/landing heights).
- Maximum height: H = v0² sin²θ / (2g).
- Mass independence: all masses fall the same way (neglecting other forces), so shots of different mass but same initial velocity follow the same trajectory.
- Energy: mechanical energy (kinetic + potential) is conserved until impact (no drag to dissipate kinetic energy).
- Practical effects: bullets or thrown objects would travel farther and straighter; there is no terminal velocity (speed can increase continuously under gravity until collision); effects like aerodynamic lift, drag, and the Magnus effect (from spin) are absent.
If you want, I can show a quick numerical example or plot for particular v0 and θ.
- Motion separates into independent horizontal and vertical components.
- Horizontal velocity is constant (no horizontal force): x(t) = v0 cosθ · t.
- Vertical motion has constant downward acceleration g: y(t) = v0 sinθ · t − ½ g t² (choose launch at y=0).
- Trajectory: the path is a parabola. With launch and landing at the same height the range R is
R = v0² sin(2θ) / g,
maximal at θ = 45°.
- Time of flight: T = 2 v0 sinθ / g (for equal launch/landing heights).
- Maximum height: H = v0² sin²θ / (2g).
- Mass independence: all masses fall the same way (neglecting other forces), so shots of different mass but same initial velocity follow the same trajectory.
- Energy: mechanical energy (kinetic + potential) is conserved until impact (no drag to dissipate kinetic energy).
- Practical effects: bullets or thrown objects would travel farther and straighter; there is no terminal velocity (speed can increase continuously under gravity until collision); effects like aerodynamic lift, drag, and the Magnus effect (from spin) are absent.
If you want, I can show a quick numerical example or plot for particular v0 and θ.
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