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A bus is moving on a straight road towards north with a uniform speed of 50km/hr.If the speed remains unchanged after turning through 90degre find the increase in the velocity of bus in turning process. pls answer with magnitude and direction?
Verified Answer
A bus is moving on a straight road towards north with a uniform speed ...
The speed is constant .i.e. acceleration =0.
Now initial velocity = u = +50j
and final velocity = v = -50i
Change in velocity ===>
v – u = -50i – 50 j = 50(-i – j) km/hr.
magnitude = 50*root2. = 70.7 km/hr.
Direction u can check as it comes:
-i-j
that is Sout west.
This question is part of UPSC exam. View all Class 11 courses
Most Upvoted Answer
A bus is moving on a straight road towards north with a uniform speed ...
Analysis:
To find the increase in velocity of the bus during the turning process, we need to consider the change in direction of the bus. Since the speed of the bus remains unchanged, the increase in velocity is solely due to the change in direction.
Initial velocity:
Magnitude: 50 km/hr
Direction: North
Change in direction:
The bus turns through 90 degrees, which means its new direction is perpendicular to its initial direction.
Final velocity:
Magnitude: 50 km/hr (unchanged)
Direction: East (perpendicular to the initial direction)
Calculating the increase in velocity:
To calculate the increase in velocity, we need to find the vector difference between the initial and final velocities.
Step 1: Converting velocities to vector form:
Initial velocity vector: 50 km/hr * (0, 1) (since it is moving towards the north)
Final velocity vector: 50 km/hr * (1, 0) (since it is now moving towards the east)
Step 2: Finding the difference between the vectors:
Final velocity vector - Initial velocity vector = (1, 0) - (0, 1) = (1-0, 0-1) = (1, -1)
Step 3: Calculating the magnitude and direction:
Magnitude of the increase in velocity = sqrt(1^2 + (-1)^2) = sqrt(2) ≈ 1.41 km/hr
Direction of the increase in velocity = arctan(-1/1) = -45 degrees (measured counterclockwise from the positive x-axis)
Therefore, the increase in velocity of the bus during the turning process is approximately 1.41 km/hr in a direction of -45 degrees (or southwest).
To find the increase in velocity of the bus during the turning process, we need to consider the change in direction of the bus. Since the speed of the bus remains unchanged, the increase in velocity is solely due to the change in direction.
Initial velocity:
Magnitude: 50 km/hr
Direction: North
Change in direction:
The bus turns through 90 degrees, which means its new direction is perpendicular to its initial direction.
Final velocity:
Magnitude: 50 km/hr (unchanged)
Direction: East (perpendicular to the initial direction)
Calculating the increase in velocity:
To calculate the increase in velocity, we need to find the vector difference between the initial and final velocities.
Step 1: Converting velocities to vector form:
Initial velocity vector: 50 km/hr * (0, 1) (since it is moving towards the north)
Final velocity vector: 50 km/hr * (1, 0) (since it is now moving towards the east)
Step 2: Finding the difference between the vectors:
Final velocity vector - Initial velocity vector = (1, 0) - (0, 1) = (1-0, 0-1) = (1, -1)
Step 3: Calculating the magnitude and direction:
Magnitude of the increase in velocity = sqrt(1^2 + (-1)^2) = sqrt(2) ≈ 1.41 km/hr
Direction of the increase in velocity = arctan(-1/1) = -45 degrees (measured counterclockwise from the positive x-axis)
Therefore, the increase in velocity of the bus during the turning process is approximately 1.41 km/hr in a direction of -45 degrees (or southwest).
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A bus is moving on a straight road towards north with a uniform speed of 50km/hr.If the speed remains unchanged after turning through 90degre find the increase in the velocity of bus in turning process. pls answer with magnitude and direction?
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A bus is moving on a straight road towards north with a uniform speed of 50km/hr.If the speed remains unchanged after turning through 90degre find the increase in the velocity of bus in turning process. pls answer with magnitude and direction? 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 bus is moving on a straight road towards north with a uniform speed of 50km/hr.If the speed remains unchanged after turning through 90degre find the increase in the velocity of bus in turning process. pls answer with magnitude and direction? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bus is moving on a straight road towards north with a uniform speed of 50km/hr.If the speed remains unchanged after turning through 90degre find the increase in the velocity of bus in turning process. pls answer with magnitude and direction?.
A bus is moving on a straight road towards north with a uniform speed of 50km/hr.If the speed remains unchanged after turning through 90degre find the increase in the velocity of bus in turning process. pls answer with magnitude and direction? 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 bus is moving on a straight road towards north with a uniform speed of 50km/hr.If the speed remains unchanged after turning through 90degre find the increase in the velocity of bus in turning process. pls answer with magnitude and direction? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bus is moving on a straight road towards north with a uniform speed of 50km/hr.If the speed remains unchanged after turning through 90degre find the increase in the velocity of bus in turning process. pls answer with magnitude and direction?.
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