Projectile Motion

Learning Objectives

  • ✦ Understand that horizontal and vertical motions are independent.
  • ✦ Calculate the trajectory's maximum height ($y_{max}$).
  • ✦ Determine the total time of flight and range.
  • ✦ Analyze how launch angle and initial velocity affect the path.

Simulation Playground

Auto-scaling graph visualization.

45°
60 m/s
9.8 m/s²
SIMULATION VIEW

Live Data

Time: 0.00 s
Max Height: 0.00 m
Distance: 0.00 m
Scale: 1.0 px/m

Key Formulas & Concepts

Horizontal Motion

In the absence of air resistance, the horizontal velocity remains constant because there is no acceleration in the horizontal direction.

$$x = v_0 \cdot \cos(\theta) \cdot t$$

Vertical Motion

Gravity acts downwards, causing a constant acceleration. This affects the vertical velocity and position over time.

$$y = v_0 \cdot \sin(\theta) \cdot t - \frac{1}{2}gt^2$$

Maximum Height

At the peak of the trajectory, the vertical velocity component is momentarily zero. This formula calculates the highest point reached.

$$y_{max} = \frac{(v_0 \cdot \sin(\theta))^2}{2g}$$

Time of Flight

The total time the projectile remains in the air, assuming it lands at the same vertical level from which it was launched.

$$T_{total} = \frac{2 \cdot v_0 \cdot \sin(\theta)}{g}$$

Knowledge Check

Question 1 of 4

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