A particle p moves from the point A(0,4) to the point (10,−4). The particle P can travel the upper-half plane {(x,y)|y≥0} at the speed of 1 m/s and the lower-halfplane{(x,y)|y≤0} at the speed of 2 m/s. The coordinates of a point on the x-axis, if the sum of the squares of the travel times of the upper- and lower-half planes is minimum, are
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a
(1,0)
b
(2,0)
c
(4,0)
d
(5,0)
answer is B.
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Detailed Solution
Let the point on the x-axis be (c,0). Sum of the squares of travel times isT=(c2+161)2+((10−c)2+162)2=c2+16+116+c2−20c4=54c2−5c+45=54(c2−4c+36)Therefore, T is minimum at c=2
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A particle p moves from the point A(0,4) to the point (10,−4). The particle P can travel the upper-half plane {(x,y)|y≥0} at the speed of 1 m/s and the lower-halfplane{(x,y)|y≤0} at the speed of 2 m/s. The coordinates of a point on the x-axis, if the sum of the squares of the travel times of the upper- and lower-half planes is minimum, are