Question

An aeroplane at an altitude of 1 km is flying horizontally at 600 km / hr, passes directly over an observer. Then the rate at which it is approaching the observer when it is 1250 meters away from him is........

• A. \(360 km/hr\)
• B. \(430 km/hr\)
• C. \(600 km/hr\)
• D. \(250 km/hr\)

Hint:

Join the plane, the observer and the point below the plane in a right triangle and differentiate the Pythagoras relation.

Answer 1

The Correct Option is A

Step 1: Approach
Use the fraction of the plane's velocity that points toward the observer.

Step 2: Geometry
The line of sight from the observer makes an angle $\theta$ with the horizontal where $\cos\theta=\dfrac{0.75}{1.25}=0.6$, because the horizontal gap is 0.75 km when the line of sight is 1.25 km (height is 1 km).

Step 3: Component
The rate at which the distance shrinks equals the speed times $\cos\theta$:
\[ 600\times0.6=360\ \text{km/h} \]
So the answer is option (A).

Final Answer:
The distance to the observer shrinks at 360 km/h, option (A). \[ \boxed{360\ \text{km/hr}} \]