Projectile Motion from Helicopter Displacement Calculation

 ❓ Question

A helicopter flying horizontally with a speed of 360 km/h at an altitude of 2 km drops an object at an instant. The object hits the ground at a point O, 20 seconds after it is dropped. Find the displacement of point O from the position of the helicopter where the object was released.

---

🖼️ Question Image

---

✍️ Short Explanation

This problem is based on:

👉 Projectile motion
👉 Horizontal velocity
👉 Resultant displacement.

Main idea:

Horizontal motion and vertical motion are independent.

Use:

$$\text{Displacement} = \sqrt{x^2+y^2}$$

---

🔷 Step 1 — Convert Speed into m/s 💯

Given:

$$360\ \text{km/h}$$

Convert into m/s:

$$360\times\frac{5}{18}$$
$$=100\ \text{m/s}$$

---

🔷 Step 2 — Horizontal Distance Covered

Horizontal velocity remains constant.

Time:

$$t=20\ \text{s}$$

Thus horizontal distance:

$$x=vt$$
$$=100\times20$$
$$=2000\ \text{m}$$
$$=2\ \text{km}$$

---

🔷 Step 3 — Vertical Distance

Altitude given:

$$2\ \text{km}$$

So vertical displacement:

$$y=2\ \text{km}$$

---

🔷 Step 4 — Resultant Displacement

Using Pythagoras theorem:

$$R=\sqrt{x^2+y^2}$$
$$=\sqrt{(2)^2+(2)^2}$$
$$=\sqrt8$$
$$=2\sqrt2\ \text{km}$$

---

🔷 Step 5 — JEE Trap Alert 🚨

❌ Speed conversion bhool jaana

❌ Horizontal and vertical motion mix kar dena

❌ Distance aur displacement confuse kar lena

Remember:

$$\boxed{ \text{Projectile motion} = \text{independent horizontal + vertical motions} }$$

---

✅ Final Answer

$$\boxed{ 2\sqrt2\ \text{km} }$$

(Option 3)

---

📚 Related Topics

• RC Circuit Phase 90° Condition
• MOI of Combined Bodies Using Parallel Axis
• Find Height Using Refraction in Layered Media