When you follow the link above, you'll find that the image shows 2 poles set up in a room with two boxes set up to run along them. Pole 1 is parallel to the west and east walls while pole 2 is parallel to the north and south walls. All measurements of each are shown in the image. Box 1 starts at the end of Pole 1 and Box 2 starts at the end of Pole 2.
- Find n (the distance between Box 2 and Box 1)
- The boxes begin running along the poles at the same time at a speed of 0.3km/h. What is the direct distance between them after two seconds?
- During the first 14 secs, calculate the smallest possible distance between the boxes while they run along the poles and the exact time at which this happens.
I calculated that the answer to the first question would be 38.4057 metres while the answer to the second question would be 25.9808 metres. However, I don't know how to work out the answer to the last question. Help would be much appreciated :)
Let the segment joining top of box 1 and box 2 be AB. Let the segment joining bottom of box 1 and box 2 be CD.
In time $t$, A and B would have moved $5t/6$.
Consider segment CD as a function of time $t$.
$CD^2(t) = (25 - 5t/6)^2 + (15-5t/6)^2$
So $AB^2(t) = (25 - 5t/6)^2 + (15-5t/6)^2 +5^2$ ... Eqn(1)
Plug $t =0$ for question $1$ and $t=2$ for Q2.
For $3$; differentiate. $-125/3 + 25t/18 -75/3 + 25t/18 =0$
You get $t=24$
But we want min distance within $14$sec. So plug $t=14$ in the distance Eqn(1)