Projectile Motion (Physics) CLASS 12 JEE MAINS

What is Projectile Motion?

Projectile motion is the motion of an object thrown into the air, moving under the effect of gravity only.

After the object is thrown:

• No engine

• No force pushing it forward

• Only gravity acts downward

This type of motion was carefully studied by Galileo Galilei.

🎯 Examples

• A ball thrown into the air

• A bullet fired from a gun

• A stone thrown at an angle

• A football kick

All follow a curved path called a parabola.

⚙️ Important Idea

Projectile motion has two separate motions happening at the same time:

1️⃣ Horizontal Motion

• Constant velocity

• No acceleration (if air resistance ignored)

2️⃣ Vertical Motion

• Accelerated motion

• Acceleration = gravity (g ≈ 9.8 m/s² downward)

👉 Horizontal and vertical motions are independent.

📐 When Object is Thrown at an Angle (θ)

Initial velocity = uuu

We divide it into two parts:

Horizontal component:

ux=ucos⁡θu_x = u \cos \thetaux=ucosθ

Vertical component:

uy=usin⁡θu_y = u \sin \thetauy=usinθ

📘 Important Formulae

1️⃣ Time of Flight (T)

T=2usin⁡θgT = \frac{2u \sin\theta}{g}T=g2usinθ

2️⃣ Maximum Height (H)

H=u2sin⁡2θ2gH = \frac{u^2 \sin^2\theta}{2g}H=2gu2sin2θ

3️⃣ Horizontal Range (R)

R=u2sin⁡2θgR = \frac{u^2 \sin 2\theta}{g}R=gu2sin2θ

🎯 Special Case

Maximum range occurs when:

θ=45∘\theta = 45^\circθ=45∘

📊 Shape of Path

The object follows a parabolic path.

Why?

• Horizontal speed constant

• Vertical speed changing

• Combination creates a curve

🧠 Very Simple Understanding

Imagine throwing a ball:

• It moves forward (horizontal motion)

• It falls downward (vertical motion)

Both together make a curved path.

🔥 Key Points Summary

• Gravity acts downward only

• Motion is 2-dimensional

• Horizontal velocity constant

• Vertical motion has acceleration