NEET Exam > NEET Questions > Airplanes A and B are flying with constant ve...
Start Learning for Free
Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 and 60 with respect to the horizontal respectively . The speed of A is 100√3 m/s . At time t=0 s; an observer in A finds B at a distance of 500m . This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t=t′ ‚ A just escape being hit by B‚ t’ (in sec) is?
Verified Answer
Airplanes A and B are flying with constant velocity in the same vertic...
For relative motion perpendicular to line of motion of A
This question is part of UPSC exam. View all NEET courses
Most Upvoted Answer
Airplanes A and B are flying with constant velocity in the same vertic...
Given Information:
- Airplanes A and B are flying in the same vertical plane.
- The angle of airplane A with respect to the horizontal is 30°.
- The angle of airplane B with respect to the horizontal is 60°.
- The speed of airplane A is 100√3 m/s.
- At time t=0s, the observer in airplane A finds airplane B at a distance of 500m.
- The observer in airplane A sees airplane B moving with a constant velocity perpendicular to the line of motion of airplane A.
Approach:
To determine when airplane A just escapes being hit by airplane B, we need to find the time it takes for airplane B to reach a position where it is closest to airplane A's path. This closest distance should be equal to the sum of the widths of the two airplanes, assuming the width of each airplane is negligible compared to the distance between them.
Solution:
Step 1: Calculate the horizontal and vertical components of the velocity of airplane A.
- The speed of airplane A is given as 100√3 m/s.
- The angle of airplane A with respect to the horizontal is 30°.
- The horizontal component of velocity (Vx) can be calculated as: Vx = V * cos(θ)
Vx = 100√3 * cos(30°) = 100√3 * √3/2 = 150 m/s
- The vertical component of velocity (Vy) can be calculated as: Vy = V * sin(θ)
Vy = 100√3 * sin(30°) = 100√3 * 1/2 = 50√3 m/s
Step 2: Calculate the horizontal and vertical components of the velocity of airplane B.
- The angle of airplane B with respect to the horizontal is 60°.
- Since the observer in airplane A sees airplane B moving with a constant velocity perpendicular to the line of motion of airplane A, the horizontal component of velocity (Vx') of airplane B should be equal to Vy.
Vx' = Vy = 50√3 m/s
- The vertical component of velocity (Vy') of airplane B should be equal to -Vx, since it is perpendicular to the line of motion of airplane A.
Vy' = -Vx = -150 m/s
Step 3: Determine the relative velocity of airplane B with respect to airplane A.
- The relative velocity (Vrel) can be calculated as the vector sum of the velocities of airplane A and airplane B.
- The horizontal component of the relative velocity (Vrel_x) can be calculated as: Vrel_x = Vx' - Vx
Vrel_x = 50√3 - 150 = -100√3 m/s
- The vertical component of the relative velocity (Vrel_y) can be calculated as: Vrel_y = Vy' - Vy
Vrel_y = -150 - 50√3 = -150 - 50√3 m/s
Step 4: Calculate the time it takes for airplane B to reach the closest distance to airplane A's path.
- The closest distance is equal to the sum of the widths of the two airplanes,
- Airplanes A and B are flying in the same vertical plane.
- The angle of airplane A with respect to the horizontal is 30°.
- The angle of airplane B with respect to the horizontal is 60°.
- The speed of airplane A is 100√3 m/s.
- At time t=0s, the observer in airplane A finds airplane B at a distance of 500m.
- The observer in airplane A sees airplane B moving with a constant velocity perpendicular to the line of motion of airplane A.
Approach:
To determine when airplane A just escapes being hit by airplane B, we need to find the time it takes for airplane B to reach a position where it is closest to airplane A's path. This closest distance should be equal to the sum of the widths of the two airplanes, assuming the width of each airplane is negligible compared to the distance between them.
Solution:
Step 1: Calculate the horizontal and vertical components of the velocity of airplane A.
- The speed of airplane A is given as 100√3 m/s.
- The angle of airplane A with respect to the horizontal is 30°.
- The horizontal component of velocity (Vx) can be calculated as: Vx = V * cos(θ)
Vx = 100√3 * cos(30°) = 100√3 * √3/2 = 150 m/s
- The vertical component of velocity (Vy) can be calculated as: Vy = V * sin(θ)
Vy = 100√3 * sin(30°) = 100√3 * 1/2 = 50√3 m/s
Step 2: Calculate the horizontal and vertical components of the velocity of airplane B.
- The angle of airplane B with respect to the horizontal is 60°.
- Since the observer in airplane A sees airplane B moving with a constant velocity perpendicular to the line of motion of airplane A, the horizontal component of velocity (Vx') of airplane B should be equal to Vy.
Vx' = Vy = 50√3 m/s
- The vertical component of velocity (Vy') of airplane B should be equal to -Vx, since it is perpendicular to the line of motion of airplane A.
Vy' = -Vx = -150 m/s
Step 3: Determine the relative velocity of airplane B with respect to airplane A.
- The relative velocity (Vrel) can be calculated as the vector sum of the velocities of airplane A and airplane B.
- The horizontal component of the relative velocity (Vrel_x) can be calculated as: Vrel_x = Vx' - Vx
Vrel_x = 50√3 - 150 = -100√3 m/s
- The vertical component of the relative velocity (Vrel_y) can be calculated as: Vrel_y = Vy' - Vy
Vrel_y = -150 - 50√3 = -150 - 50√3 m/s
Step 4: Calculate the time it takes for airplane B to reach the closest distance to airplane A's path.
- The closest distance is equal to the sum of the widths of the two airplanes,
Community Answer
Airplanes A and B are flying with constant velocity in the same vertic...
5 second
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
|
|
Explore Courses for NEET exam
|
|
Similar NEET Doubts
Top Courses for NEETView all
Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 and 60 with respect to the horizontal respectively . The speed of A is 100√3 m/s . At time t=0 s; an observer in A finds B at a distance of 500m . This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t=t′ ‚ A just escape being hit by B‚ t’ (in sec) is?
Question Description
Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 and 60 with respect to the horizontal respectively . The speed of A is 100√3 m/s . At time t=0 s; an observer in A finds B at a distance of 500m . This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t=t′ ‚ A just escape being hit by B‚ t’ (in sec) is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 and 60 with respect to the horizontal respectively . The speed of A is 100√3 m/s . At time t=0 s; an observer in A finds B at a distance of 500m . This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t=t′ ‚ A just escape being hit by B‚ t’ (in sec) is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 and 60 with respect to the horizontal respectively . The speed of A is 100√3 m/s . At time t=0 s; an observer in A finds B at a distance of 500m . This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t=t′ ‚ A just escape being hit by B‚ t’ (in sec) is?.
Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 and 60 with respect to the horizontal respectively . The speed of A is 100√3 m/s . At time t=0 s; an observer in A finds B at a distance of 500m . This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t=t′ ‚ A just escape being hit by B‚ t’ (in sec) is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 and 60 with respect to the horizontal respectively . The speed of A is 100√3 m/s . At time t=0 s; an observer in A finds B at a distance of 500m . This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t=t′ ‚ A just escape being hit by B‚ t’ (in sec) is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 and 60 with respect to the horizontal respectively . The speed of A is 100√3 m/s . At time t=0 s; an observer in A finds B at a distance of 500m . This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t=t′ ‚ A just escape being hit by B‚ t’ (in sec) is?.
Solutions for Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 and 60 with respect to the horizontal respectively . The speed of A is 100√3 m/s . At time t=0 s; an observer in A finds B at a distance of 500m . This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t=t′ ‚ A just escape being hit by B‚ t’ (in sec) is? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 and 60 with respect to the horizontal respectively . The speed of A is 100√3 m/s . At time t=0 s; an observer in A finds B at a distance of 500m . This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t=t′ ‚ A just escape being hit by B‚ t’ (in sec) is? defined & explained in the simplest way possible. Besides giving the explanation of
Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 and 60 with respect to the horizontal respectively . The speed of A is 100√3 m/s . At time t=0 s; an observer in A finds B at a distance of 500m . This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t=t′ ‚ A just escape being hit by B‚ t’ (in sec) is?, a detailed solution for Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 and 60 with respect to the horizontal respectively . The speed of A is 100√3 m/s . At time t=0 s; an observer in A finds B at a distance of 500m . This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t=t′ ‚ A just escape being hit by B‚ t’ (in sec) is? has been provided alongside types of Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 and 60 with respect to the horizontal respectively . The speed of A is 100√3 m/s . At time t=0 s; an observer in A finds B at a distance of 500m . This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t=t′ ‚ A just escape being hit by B‚ t’ (in sec) is? theory, EduRev gives you an
ample number of questions to practice Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 and 60 with respect to the horizontal respectively . The speed of A is 100√3 m/s . At time t=0 s; an observer in A finds B at a distance of 500m . This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t=t′ ‚ A just escape being hit by B‚ t’ (in sec) is? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup