First slide
Equation of line in Straight lines
Question

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)|y0} at the speed of 1 m/s and the lower-halfplane{(x,y)|y0} 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

Moderate
Solution

Let the point on the x-axis be (c,0). Sum of the squares of travel times is

T=(c2+161)2+((10c)2+162)2

=c2+16+116+c220c4=54c25c+45=54(c24c+36)

Therefore, T is minimum at c=2

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