Question

An aeroplane leaves an airport and flies due north at a speed of $1000 \mathrm{~km}$ per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of $1200 \mathrm{~km}$ per hour. How far apart will be the two planes after $1 \frac{1}{1}$ hours?

Name: Problem 11, Chapter 6: NCERT Class 10 - Math
Uploaded: 2021-06-29T01:06:52-08:00
Duration: 3 min 59 s
Channel: Suman Saurav Thakur
Description: An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1 (1)/(1) hours?

   An aeroplane leaves an airport and flies due north at a speed of $1000 \mathrm{~km}$ per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of $1200 \mathrm{~km}$ per hour. How far apart will be the two planes after $1 \frac{1}{1}$ hours?

NCERT Class 10 - Math

Parvin Sinclair,… 1st Edition

Chapter 6, Problem 11

Instant Answer

Solved by Expert Suman Saurav Thakur

06/29/2021

Step 1

The distance travelled by the first airplane in 1.5 hours is given by speed multiplied by time, which is $1000 \times 1.5 = 1500$ km. Similarly, the distance travelled by the second airplane in the same time is $1200 \times 1.5 = 1800$ km. Show more…

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An aeroplane leaves an airport and flies due north at a speed of $1000 \mathrm{~km}$ per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of $1200 \mathrm{~km}$ per hour. How far apart will be the two planes after $1 \frac{1}{1}$ hours?

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Key Concepts

Uniform Motion

This concept refers to movement at a constant speed in a specific direction, where the distance traveled is directly proportional to the time elapsed. It is fundamental in calculating displacement when speed remains unchanging over time.

Pythagorean Theorem

A key principle in geometry that applies to right-angled triangles, the Pythagorean theorem allows one to determine the length of the hypotenuse when the lengths of the other two perpendicular sides are known. This is critical for finding the distance between two objects moving in orthogonal directions.

Relative Displacement

This concept involves analyzing the positions of two objects moving away from a common starting point in different directions. By treating each movement as a vector component, one can combine them geometrically using the Pythagorean theorem to determine the overall separation between the objects.

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