An aeroplane leaves an Airport and flies due North at 300 km/h. At the same time, another aeroplane leaves the same Airport and flies due West at 400 km/h. How far apart the two aeroplanes would be after 1½ hours
Solution:
Given, an aeroplane leaves an airport and flies due North at 300km/h
Another aeroplane leaves the same airport at the same time and flies due West at 400km/hr.
We have to find the distance between two aeroplanes after 1½ hours.
We know that, Distance = Speed × Time
Distance travelled by aeroplane which flies due North in 1½ hours,
Time = (2 + 1)/2 = 3/2 hours
Distance = 300 × 3/2 = 150 × 3 = 450 km
Distance travelled by aeroplane which flies due West in 1½ hours,
Distance = 400 × 3/2 = 200 × 3 = 600 km
From the above figure,
OA is the distance travelled by the plane flying due North
OB is the distance travelled by the plane flying due West
The triangle OAB represents a right triangle with O at the right triangle.
By using pythagoras theorem,
AB2 = OA2 + OB2
AB2 = (450)2 + (600)2
AB2 = 202500 + 360000
AB2 = 562500
Taking square root,
AB = 750 km
Therefore, the two aeroplanes are 750 km apart in 1½ hours.
✦ Try This: An aeroplane leaves an Airport and flies due South at 200 km/h. At the same time, another aeroplane leaves the same Airport and flies due East at 300 km/h. How far apart the two aeroplanes would be after 1½ hours
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.4 Sample Problem 3
An aeroplane leaves an Airport and flies due North at 300 km/h. At the same time, another aeroplane leaves the same Airport and flies due West at 400 km/h. How far apart the two aeroplanes would be after 1½ hours
Summary:
An aeroplane leaves an Airport and flies due North at 300 km/h. At the same time, another aeroplane leaves the same Airport and flies due West at 400 km/h. The two aeroplanes would be 750 km apart after 1½ hours
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