SOLUTION: There's a square with ABCD(clockwise). One side is 67m long. Object 1 starts moving from point A towards point B with a speed of 5.9m/s(unchanging). Object 2 remains at point D. Ho

Question 1053844: There's a square with ABCD(clockwise). One side is 67m long. Object 1 starts moving from point A towards point B with a speed of 5.9m/s(unchanging). Object 2 remains at point D. How fast(m/s) does the distance DX between the two objects change, when X is 62m from point A?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let D be the length of the diagonal. l be length and w be width, then
:
By Pythagoras
:
D^2 = l^2 + w^2
:
differentiate implicitly
:
2D*(dl/dt) = 2l*(dl/dt) + 2w*(dw/dt)
:
note that dw/dt is 0, that is, does not change
:
D *(dD/dt) = 2l*(dl/dt)
:
dD/dt = 2(62)*(5.9) / (62^2 + 67^2)^(1/2) = 8.01 m/s
:
*****************************************************************
Distance from object 1 to object2 is changing at 8.01 m/s when
object 1 is 62 m from Point A
*****************************************************************
:

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