A person standing on the ground at point A saw an object at point B on the ground at a distance of 600 meters. The object started flying towards him at an angle of 30° with the ground. The person saw the object for the second time at point C flying at 30° angle with him. At point C, the object changed direction and continued flying upwards. The person saw the object for the third time when the object was directly above him. The object was flying at a constant speed of 10 kmph.
Find the angle at which the object was flying after the person saw it for the second time. You may use additional statement(s) if required.
Statement I: After changing direction the object took 3 more minutes than it had taken before. Statement II: After changing direction the object travelled an additional 200√3 meters.
Which of the following is the correct option?
Explanation:
From the given data,
m∠CAB = 30°; m∠CBA = 30° and AB = 600 m
∴ BC = AC = 200√3 m … [By sine rule]
Statement I: After changing the direction the object took 3 more minutes than it had taken before.
The object travels 200√3 m from B to C at 10 km/hr
Thus, in 3 minutes it can travel 500 m. Hence, the object travels a total of 500 + 200√3m from C.
Thus, we know the hypotenuse CD by which we can find out the angle.
Statement II: After changing directions, the object travels 200√3 m.
Since, the object travels the same distance as before, this can only happen if the object stays on the course as before without changing any direction.
Thus, we can clearly see that the two angles from the statements are inconsistent with each other.
Hence, option (d).
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