Mecânica e máquinas simples · AP Physics 1 Unit 1 (2D Kinematics)
Simulador de lançamento oblíquo e projéteis
Simulador de lançamento oblíquo e trajetória de projéteis: alcance e altura máxima
- No navegador
- Sem cadastro
- Dedução ao vivo
- Modo projetor
- Folha de exercícios A4
Janela de simulação 3D● 60 FPS
Variáveis de controle do experimento
m/s
°
m
m/s²
Deduções e métricas em tempo real
Tempo de voo t
--
Altura máxima H
--
Alcance horizontal X
--
Velocidade de impacto
--
Dedução de fórmulas em tempo real
Fórmula fundamental:
--Substituição de valores:
--Estado físico: --
Exemplos clássicos e armadilhas de exame
Worked Problem
Problema: A rock is thrown horizontally from a 20m cliff at 15m/s. Find flight time and horizontal range. (g=10m/s²)
Derivação passo a passo:
- Vertical fall: h = 0.5gt² => t = sqrt(40/10) = 2s. Horizontal range: X = vx*t = 15*2 = 30m.
Worked Problem
Problema: A ball is kicked at 20m/s at 30° to horizontal. Find max apex height and total range. (g=10m/s²)
Derivação passo a passo:
- vy = 20*sin30° = 10m/s, vx = 10sqrt(3) m/s. Apex height H = 10²/(2*10) = 5m. Flight time t = 2s. Range X = 20sqrt(3) ≈ 34.64m.
Folha de investigação em aula e exercícios
Q1. Variant 1: What is the constant ratio between velocity angle tangent tanθ and displacement angle tangent tanα?
Answer Key: tanθ = gt/v0 and tanα = 0.5gt/v0. Thus tanθ = 2 tanα, meaning velocity angle tangent is strictly twice displacement angle tangent.
Q2. Variant 2: When launched from an elevated cliff (h > 0), is the optimal angle for maximum range still 45°?
Answer Key: Less than 45°. The extra vertical drop extends flight time, so prioritizing horizontal speed yields greater range.
Q3. Variant 3: Why is a level bomber directly above its dropped bomb at detonation neglecting drag?
Answer Key: Both the airplane and the bomb maintain the exact same horizontal velocity by inertia.
Perguntas frequentes e erros comuns
What does the dual-ball drop experiment prove?
It proves that vertical motion in projectile trajectory is identical to free fall and completely independent of horizontal speed.
How does air resistance alter real-world trajectories?
Air drag reduces range, steepens descent trajectory, and lowers the optimal launch angle from 45° to approximately 38°-42°.
Is projectile motion uniformly accelerated motion?
Yes! Because gravity is constant, acceleration is constant (a = g downward), making it uniformly accelerated curvilinear motion.
Will a dart aimed directly at a monkey hit if the monkey drops at launch?
Yes, always (before hitting ground)! Both dart and monkey accelerate downward at g, maintaining the line of sight.