Question

A drone is flying due west, a little above the train, with a speed of 10 m/s. A 270 meter long train is moving due east at a speed of 20 m/s. The time taken by the drone to cross the train is:

• A. 27 s
• B. 13.5 s
• C. 20 s
• D. 9 s

Hint:

To calculate the time taken for one object to cross another, use the formula \( t = \frac{\text{Distance}}{\text{Relative Speed}} \). The relative speed is the sum of their individual speeds when they are moving in opposite directions.

Answer 1

The Correct Option is D

To solve this problem, we first need to calculate the relative speed between the drone and the train. Since the drone is flying due west and the train is moving due east, the relative speed is the sum of their individual speeds.
- Speed of the drone \( v_{\text{drone}} = 10 \, \text{m/s} \) (westward), - Speed of the train \( v_{\text{train}} = 20 \, \text{m/s} \) (eastward).
The relative speed between the drone and the train is: \[ v_{\text{relative}} = v_{\text{drone}} + v_{\text{train}} = 10 + 20 = 30 \, \text{m/s} \] Now, the time taken for the drone to cross the train is given by the formula: \[ t = \frac{\text{Distance}}{\text{Relative Speed}} \] The distance to be covered is the length of the train, which is 270 m. Thus, the time taken by the drone to cross the train is: \[ t = \frac{270 \, \text{m}}{30 \, \text{m/s}} = 9 \, \text{s} \] Thus, the time taken by the drone to cross the train is \( 9 \, \text{s} \).