Projectile Motion Interactive Trajectory Lab

Explore parabolic motion under gravity (g = 9.8 m/s²). Tweak launch angle θ and initial velocity u to observe trajectory changes, find the angle for maximum range (45°), and solve numericals with real-time stats.

2D Kinematics Trajectory LabLive Vector Engine

g = 9.8 m/s² (Earth gravity)

Launch Angle (θ):

45°

Initial Velocity (u):

25 m/s

Horizontal Range (R)63.8 m

Max Height (H_max)15.9 m

Time of Flight (T)3.61 s

Range: R = (u² · sin 2θ) / gMax Height: H = (u² · sin² θ) / 2gTime: T = (2u · sin θ) / g

CBSE Physics Foundation: Derivations & Key Results

A projectile is any object thrown into space upon which the only acting force is gravity. The horizontal motion has constant velocity ($u_x = u \cos \theta$, $a_x = 0$), while vertical motion is under constant acceleration ($a_y = -g$).

Important CBSE Exam Takeaways:

1. Maximum Range Condition: The range $R$ is maximum when $\sin 2\theta = 1 \implies 2\theta = 90^\circ \implies \theta = 45^\circ$. Maximum Range R_max = u² / g.
2. Complementary Angles: Two angles of projection with the same initial velocity produce the same horizontal range if $\theta_1 + \theta_2 = 90^\circ$ (e.g. $30^\circ$ and $60^\circ$).
3. Velocity at Highest Point: At the peak of trajectory, the vertical velocity $v_y = 0$, but the horizontal velocity is still $u_x = u \cos \theta$. Hence, the kinetic energy is not zero at the apex!

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