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