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A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30* , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60*. Find the time taken by the car to reach the foot of the tower from this point.?
Most Upvoted Answer
A straight highway leads to the foot of a tower. A man standing at the...
Let the distance traveled by the car in 6seconds=AB=X metres
Height of the tower CD=h metres
The remaining distance to be traveled by the car BC =d metres
AC =AB+BC=x+d metres
ANGLE PDA=ANGLE DAC=30
ANGLE PDB=ANGLE DB*C=60
TRIANGLE BCD TAN60=CD/BC=root3=h/d
h=root3d
TRIANGLE ACD TAN30=CD/AC
1/root3=h/(x+d)
h=(x+d)/root3
(x+d)/root3=root3d
x+d=3d
x=2d
d=x/2
Time taken to travel x metres =6seconds
Time taken to travel the distance of D metres i. e., x/2=6/2=3seconds
I'm
THX for asking ...keep learning G 😉🤣🤣
Height of the tower CD=h metres
The remaining distance to be traveled by the car BC =d metres
AC =AB+BC=x+d metres
ANGLE PDA=ANGLE DAC=30
ANGLE PDB=ANGLE DB*C=60
TRIANGLE BCD TAN60=CD/BC=root3=h/d
h=root3d
TRIANGLE ACD TAN30=CD/AC
1/root3=h/(x+d)
h=(x+d)/root3
(x+d)/root3=root3d
x+d=3d
x=2d
d=x/2
Time taken to travel x metres =6seconds
Time taken to travel the distance of D metres i. e., x/2=6/2=3seconds
I'm
THX for asking ...keep learning G 😉🤣🤣
Community Answer
A straight highway leads to the foot of a tower. A man standing at the...
Given Information:
- The angle of depression of the car from the top of the tower is 30° initially.
- Six seconds later, the angle of depression of the car is 60°.
- The car is approaching the foot of the tower with a uniform speed.
Approach:
1. We can use trigonometry to solve this problem.
2. Let's assume the height of the tower is 'h' and the distance of the car from the foot of the tower at the initial observation is 'x'.
3. Using the angle of depression of 30°, we can write the equation: tan(30°) = h/x.
4. After 6 seconds, the car is closer to the tower, and the angle of depression is 60°. Let's assume the distance covered by the car in these 6 seconds is 'd'.
5. Using the angle of depression of 60°, we can write the equation: tan(60°) = h/(x-d).
Solving the Equations:
1. From the first equation, we get: x = h/tan(30°).
2. Substituting this value of x in the second equation, we get: tan(60°) = h/(h/tan(30°)-d).
3. Simplifying further, we get: √3 = tan(30°)/(1 - (d/h*tan(30°))).
4. Rearranging the equation, we get: √3 - √3(d/h*tan(30°)) = tan(30°).
5. Dividing both sides of the equation by √3, we get: 1 - d/h*tan(30°) = 1/√3.
6. Rearranging again, we get: d/h*tan(30°) = 1 - 1/√3.
7. Simplifying, we get: d/h = (√3 - 1)/(√3*tan(30°)).
8. Using the values of √3 and tan(30°), we get: d/h = (√3 - 1)/(√3*(1/√3)).
9. Simplifying further, we get: d/h = (√3 - 1).
Conclusion:
- The ratio of the distance covered by the car in 6 seconds to the height of the tower is (√3 - 1).
- This means the car covers a distance (√3 - 1) times the height of the tower in 6 seconds.
- Therefore, the time taken by the car to reach the foot of the tower from the point of observation is 6 seconds.
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A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30* , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60*. Find the time taken by the car to reach the foot of the tower from this point.?
Question Description
A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30* , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60*. Find the time taken by the car to reach the foot of the tower from this point.? 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 straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30* , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60*. Find the time taken by the car to reach the foot of the tower from this point.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30* , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60*. Find the time taken by the car to reach the foot of the tower from this point.?.
A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30* , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60*. Find the time taken by the car to reach the foot of the tower from this point.? 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 straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30* , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60*. Find the time taken by the car to reach the foot of the tower from this point.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30* , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60*. Find the time taken by the car to reach the foot of the tower from this point.?.
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A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30* , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60*. Find the time taken by the car to reach the foot of the tower from this point.?, a detailed solution for A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30* , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60*. Find the time taken by the car to reach the foot of the tower from this point.? has been provided alongside types of A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30* , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60*. Find the time taken by the car to reach the foot of the tower from this point.? theory, EduRev gives you an
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