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A bird is sitting on the top of a tree which is 80 m high. The angle of elevation of the bird from a point on the ground is 45 degree. The bird flies away from the point of observation horizontally and remains at constant height. After 2 sec the angle of elevation of the bird from the point of observation becomes 30 degree. Find the speed of the flying bird. (Explain it step by step)?
Most Upvoted Answer
A bird is sitting on the top of a tree which is 80 m high. The angle o...
Hi guys
draw the diagram.. here are the steps...
triangle ACB
tan 45 degree = 80/y
1= 80/y
y=80m ---------(1)
triangle DEB
tan 30 degree = 80/x
1/ root 3= 80/x
x= 80 root3 --------(2)
from 1 and 2 we get
80root3 - 80
80(root3-1)m
speed of the bird= 2 sec
80(root3-1)/2
2 and 80 we get cancelled that will give us 40
40(root3-1)
SORRY I KNOW TILL THIS MUCH CAN SOMEONE PLZ TILL ME THE NEXT STEP
40(root3-1)*60 * 60/1000
cancell the zeroes
144(root3-1)
IF THERE IS ANY MISTAKE PLZ LET ME KNOW....
Community Answer
A bird is sitting on the top of a tree which is 80 m high. The angle o...
**Solution:**
Let's break down the problem step by step:
1. **Identify the given information**:
- Height of the tree (h) = 80 m
- Initial angle of elevation (θ1) = 45 degrees
- Final angle of elevation (θ2) = 30 degrees
- Time taken (t) = 2 seconds
2. **Draw a diagram**:
- Draw a triangle ABC, where A represents the point of observation on the ground, B represents the initial position of the bird, and C represents the final position of the bird after 2 seconds.
- AB represents the height of the tree, BC represents the horizontal distance covered by the bird, and AC represents the length of the bird's flight path.
3. **Find the distance covered by the bird horizontally (BC)**:
- Since the bird flies horizontally, BC remains constant.
- We can use the formula: BC = v*t, where v is the speed of the bird and t is the time taken.
- Substitute the given values: BC = v * 2
4. **Find the height of the bird at the final position (h2)**:
- In triangle ABC, tan(θ1) = AB/BC (using the initial angle of elevation)
- Substitute the values: tan(45) = 80/BC
- Rearrange the equation to solve for BC: BC = 80/tan(45)
5. **Substitute the value of BC in terms of v into the equation from step 3**:
- BC = v * 2
- Substitute the value of BC from step 4: 80/tan(45) = v * 2
- Simplify the equation: 80√2 = 2v
- Divide both sides by 2: v = 40√2
6. **Calculate the speed of the flying bird**:
- Use a calculator to find the approximate value of v: v ≈ 56.57 m/s
7. **Final Answer**:
- The speed of the flying bird is approximately 56.57 m/s.
Let's break down the problem step by step:
1. **Identify the given information**:
- Height of the tree (h) = 80 m
- Initial angle of elevation (θ1) = 45 degrees
- Final angle of elevation (θ2) = 30 degrees
- Time taken (t) = 2 seconds
2. **Draw a diagram**:
- Draw a triangle ABC, where A represents the point of observation on the ground, B represents the initial position of the bird, and C represents the final position of the bird after 2 seconds.
- AB represents the height of the tree, BC represents the horizontal distance covered by the bird, and AC represents the length of the bird's flight path.
3. **Find the distance covered by the bird horizontally (BC)**:
- Since the bird flies horizontally, BC remains constant.
- We can use the formula: BC = v*t, where v is the speed of the bird and t is the time taken.
- Substitute the given values: BC = v * 2
4. **Find the height of the bird at the final position (h2)**:
- In triangle ABC, tan(θ1) = AB/BC (using the initial angle of elevation)
- Substitute the values: tan(45) = 80/BC
- Rearrange the equation to solve for BC: BC = 80/tan(45)
5. **Substitute the value of BC in terms of v into the equation from step 3**:
- BC = v * 2
- Substitute the value of BC from step 4: 80/tan(45) = v * 2
- Simplify the equation: 80√2 = 2v
- Divide both sides by 2: v = 40√2
6. **Calculate the speed of the flying bird**:
- Use a calculator to find the approximate value of v: v ≈ 56.57 m/s
7. **Final Answer**:
- The speed of the flying bird is approximately 56.57 m/s.
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A bird is sitting on the top of a tree which is 80 m high. The angle of elevation of the bird from a point on the ground is 45 degree. The bird flies away from the point of observation horizontally and remains at constant height. After 2 sec the angle of elevation of the bird from the point of observation becomes 30 degree. Find the speed of the flying bird. (Explain it step by step)?
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A bird is sitting on the top of a tree which is 80 m high. The angle of elevation of the bird from a point on the ground is 45 degree. The bird flies away from the point of observation horizontally and remains at constant height. After 2 sec the angle of elevation of the bird from the point of observation becomes 30 degree. Find the speed of the flying bird. (Explain it step by step)? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A bird is sitting on the top of a tree which is 80 m high. The angle of elevation of the bird from a point on the ground is 45 degree. The bird flies away from the point of observation horizontally and remains at constant height. After 2 sec the angle of elevation of the bird from the point of observation becomes 30 degree. Find the speed of the flying bird. (Explain it step by step)? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bird is sitting on the top of a tree which is 80 m high. The angle of elevation of the bird from a point on the ground is 45 degree. The bird flies away from the point of observation horizontally and remains at constant height. After 2 sec the angle of elevation of the bird from the point of observation becomes 30 degree. Find the speed of the flying bird. (Explain it step by step)?.
A bird is sitting on the top of a tree which is 80 m high. The angle of elevation of the bird from a point on the ground is 45 degree. The bird flies away from the point of observation horizontally and remains at constant height. After 2 sec the angle of elevation of the bird from the point of observation becomes 30 degree. Find the speed of the flying bird. (Explain it step by step)? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A bird is sitting on the top of a tree which is 80 m high. The angle of elevation of the bird from a point on the ground is 45 degree. The bird flies away from the point of observation horizontally and remains at constant height. After 2 sec the angle of elevation of the bird from the point of observation becomes 30 degree. Find the speed of the flying bird. (Explain it step by step)? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bird is sitting on the top of a tree which is 80 m high. The angle of elevation of the bird from a point on the ground is 45 degree. The bird flies away from the point of observation horizontally and remains at constant height. After 2 sec the angle of elevation of the bird from the point of observation becomes 30 degree. Find the speed of the flying bird. (Explain it step by step)?.
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A bird is sitting on the top of a tree which is 80 m high. The angle of elevation of the bird from a point on the ground is 45 degree. The bird flies away from the point of observation horizontally and remains at constant height. After 2 sec the angle of elevation of the bird from the point of observation becomes 30 degree. Find the speed of the flying bird. (Explain it step by step)?, a detailed solution for A bird is sitting on the top of a tree which is 80 m high. The angle of elevation of the bird from a point on the ground is 45 degree. The bird flies away from the point of observation horizontally and remains at constant height. After 2 sec the angle of elevation of the bird from the point of observation becomes 30 degree. Find the speed of the flying bird. (Explain it step by step)? has been provided alongside types of A bird is sitting on the top of a tree which is 80 m high. The angle of elevation of the bird from a point on the ground is 45 degree. The bird flies away from the point of observation horizontally and remains at constant height. After 2 sec the angle of elevation of the bird from the point of observation becomes 30 degree. Find the speed of the flying bird. (Explain it step by step)? theory, EduRev gives you an
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