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Physics · Kinematics

Projectile Motion Simulator

Adjust the launch speed and angle, watch the cannonball fly, and see exactly how range, max height, and time of flight change in real time.

Try the simulator See the formula FAQs

🚀 Projectile Motion Simulator

Kinematics
What's happening? The cannonball follows a parabolic path. Range = u²sin2θ/g. Try 45° for maximum range. Notice how the velocity components vx and vy change during flight.
Why this matters for JEE

Projectile motion is the most-tested kinematics concept in JEE Main.

Every year, 1-2 questions come directly from projectile motion. The key is understanding that horizontal and vertical motion are independent — gravity only affects the vertical component.

Key formulas

Projectile Motion Formulas

Range

R = u²sin2θ/g

Maximum at θ = 45°

Max Height

H = u²sin²θ/2g

Maximum at θ = 90°

Time of Flight

T = 2u·sinθ/g

Independent of horizontal motion

Horizontal Velocity

vx = u·cosθ (constant)

Gravity doesn't affect vx

Step-by-step problem solving

How to solve projectile motion problems in JEE

  1. Resolve initial velocity — v₀ₓ = u cos θ, v₀ᵧ = u sin θ. Horizontal and vertical components are independent.
  2. Choose axis/sign convention — upward = +, rightward = +. Gravity g = -9.8 m/s² in vertical direction.
  3. Apply kinematic equations — x = v₀ₓt, y = v₀ᵧt + ½gt², vᵧ = v₀ᵧ + gt. Use time t consistently.
  4. For max range — set θ = 45° — R = u²sin2θ/g is max when sin2θ = 1, so 2θ = 90°, θ = 45°.
  5. Check if launched from height — use y = v₀ᵧt - ½gt² and solve for t when y = -h.
Common JEE mistakes

What students get wrong

❌ Forgetting vx is constant

Horizontal velocity never changes (no air resistance). Only vy changes due to gravity.

❌ Using 45° for max height

45° gives max RANGE. 90° gives max HEIGHT. These are different!

❌ Mixing up sin and cos

Range uses sin2θ. Height uses sin²θ. Time uses sinθ. One letter difference changes everything.

❌ Ignoring the sign of g

g is negative when the projectile moves up, positive when it comes down. Set up your sign convention first.

FAQs

Projectile Motion Questions

Why is 45° the angle for maximum range?

Range R = u²sin2θ/g. sin2θ is maximum when 2θ = 90°, so θ = 45°. At this angle, the horizontal and vertical components of velocity are perfectly balanced.

Does mass affect projectile motion?

No! Without air resistance, mass doesn't appear in any projectile formula. A feather and a cannonball follow the same path in a vacuum.

What if the projectile is launched from a height?

Then you can't use the simple range formula. You need to solve the vertical equation s = ut + ½at² with the initial height, then find when y = 0.

Is horizontal velocity really constant?

Yes, in ideal projectile motion (no air resistance). Gravity acts only vertically, so vx = u·cosθ stays the same throughout the flight.

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