Projectile Motion Simulator प्रक्षेप्य गति
JEE Main / NEET Physics Unit 2: Kinematics · NCERT Class 11 Physics, Motion in a Plane · SLH original
⚠️ Simulated values from the model below — not real lab measurements.
Readings — position and velocity during the flight
| t (s) | x (m) | y (m) | vₓ (m/s) | v_y (m/s) |
|---|
Guided experiment — step by step
- Keep u = 20 m/s, h = 0. Launch at 15°, 30°, 45°, 60°, 75° (press Launch each time — the last 3 paths stay as dotted lines).
- Which angle gives the longest range? Which two angles give the same range?
- Now set h = 20 m. Is 45° still the best angle? (Try 35°–40°.)
- Change g to Moon. By how many times does the range grow? Compare with R ∝ 1/g.
Formula, units & assumptions
uₓ = u cos θ (stays constant) · u_y = u sin θ · x = uₓ t · y = h + u_y t − ½ g t²
Time of flight T = [u_y + √(u_y² + 2gh)] / g → for h = 0: T = 2u sin θ / g
Range R = uₓ T → for h = 0: R = u² sin 2θ / g · Max height H = h + u² sin²θ / 2g
Units: length in metres (m), time in seconds (s), speed in m/s, g in m/s², angles in degrees on screen (radians inside formulas).
Assumptions & limits of the model: No air resistance · g is constant and points straight down · flat ground · the ball is a point (no spin). Real balls go a shorter distance because of air drag.
Exam connection — questions
Concept check (MCQ)
1. With no air resistance and level ground, which launch angle gives the maximum range for a fixed speed?
2. Two balls are thrown with the same speed at 30° and 60° on level ground. Their ranges are:
3. At the highest point of the path, the velocity and acceleration of the ball are:
Numerical answer (type a number)
A ball is thrown with u = 20 m/s at 30° on level ground (g = 10 m/s²). Find the time of flight in seconds.
A ball is thrown with u = 20 m/s at 45° on level ground (g = 10 m/s²). Find the range in metres.
A ball is thrown straight up (θ = 90°) with u = 20 m/s (g = 10 m/s²). Find the maximum height in metres.