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A car A is going north-east at 80km/h and another car B is going south-east at 60km/h. The direction of the relative velocity of A with B makes an angle of x with north find tan x?
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A car A is going north-east at 80km/h and another car B is going south...
Given:
Car A is going north-east at 80 km/h
Car B is going south-east at 60 km/h
To find:
The direction of the relative velocity of car A with car B makes an angle x with north. Find tan x.
Solution:
Let us consider the two cars A and B as shown in the figure below:
The velocity of car A can be resolved into two components:
1. Velocity towards north = 80/sqrt(2) km/h (since it is moving at 45 degrees to the north direction)
2. Velocity towards east = 80/sqrt(2) km/h (since it is moving at 45 degrees to the east direction)
Similarly, the velocity of car B can be resolved into two components:
1. Velocity towards south = 60/sqrt(2) km/h (since it is moving at 45 degrees to the south direction)
2. Velocity towards east = 60/sqrt(2) km/h (since it is moving at 45 degrees to the east direction)
The relative velocity of car A with respect to car B can be found by subtracting the velocity of car B from the velocity of car A:
1. Velocity towards north-east = (80/sqrt(2) - 60/sqrt(2)) km/h = 20/sqrt(2) km/h
The direction of the relative velocity of car A with respect to car B makes an angle x with north. This angle can be found as follows:
tan x = (Velocity towards north-east) / (Velocity towards north)
tan x = (20/sqrt(2)) / (80/sqrt(2))
tan x = 1/4
tan x = 0.25
Therefore, the direction of the relative velocity of car A with respect to car B makes an angle of tan^-1(0.25) with north.
Car A is going north-east at 80 km/h
Car B is going south-east at 60 km/h
To find:
The direction of the relative velocity of car A with car B makes an angle x with north. Find tan x.
Solution:
Let us consider the two cars A and B as shown in the figure below:
The velocity of car A can be resolved into two components:
1. Velocity towards north = 80/sqrt(2) km/h (since it is moving at 45 degrees to the north direction)
2. Velocity towards east = 80/sqrt(2) km/h (since it is moving at 45 degrees to the east direction)
Similarly, the velocity of car B can be resolved into two components:
1. Velocity towards south = 60/sqrt(2) km/h (since it is moving at 45 degrees to the south direction)
2. Velocity towards east = 60/sqrt(2) km/h (since it is moving at 45 degrees to the east direction)
The relative velocity of car A with respect to car B can be found by subtracting the velocity of car B from the velocity of car A:
1. Velocity towards north-east = (80/sqrt(2) - 60/sqrt(2)) km/h = 20/sqrt(2) km/h
The direction of the relative velocity of car A with respect to car B makes an angle x with north. This angle can be found as follows:
tan x = (Velocity towards north-east) / (Velocity towards north)
tan x = (20/sqrt(2)) / (80/sqrt(2))
tan x = 1/4
tan x = 0.25
Therefore, the direction of the relative velocity of car A with respect to car B makes an angle of tan^-1(0.25) with north.
Community Answer
A car A is going north-east at 80km/h and another car B is going south...
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A car A is going north-east at 80km/h and another car B is going south-east at 60km/h. The direction of the relative velocity of A with B makes an angle of x with north find tan x?
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A car A is going north-east at 80km/h and another car B is going south-east at 60km/h. The direction of the relative velocity of A with B makes an angle of x with north find tan x? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A car A is going north-east at 80km/h and another car B is going south-east at 60km/h. The direction of the relative velocity of A with B makes an angle of x with north find tan x? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car A is going north-east at 80km/h and another car B is going south-east at 60km/h. The direction of the relative velocity of A with B makes an angle of x with north find tan x?.
A car A is going north-east at 80km/h and another car B is going south-east at 60km/h. The direction of the relative velocity of A with B makes an angle of x with north find tan x? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A car A is going north-east at 80km/h and another car B is going south-east at 60km/h. The direction of the relative velocity of A with B makes an angle of x with north find tan x? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car A is going north-east at 80km/h and another car B is going south-east at 60km/h. The direction of the relative velocity of A with B makes an angle of x with north find tan x?.
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