How to Solve a Related Rates Problem Involving a Moving Box and Truck

[kingwinner]

1) (Related Rates) One end of a rope 20 meters long is attached to a box resting on the floor. The other end is passed over a pulley directly above the box, 5 meters above the floor, and attached to the back of a truck at a point 1 meters above the ground. The truck then drives in a straight line away from the pulley at a speed of 0.5 m/s. At what speed is the box rising when the top of the box is 2 meters above the ground?


I really don't get this problem. I can't even start doing the calcultions because I am not sure how to set up the variables in the problem...can someone please give me some guidelines/hints?

Thanks a lot!

 

[Noober]

It's a triangle: (not to scale)

Pulley
 |\
4| \15
 |__\Truck
1| X
Box

With dx/dt=0.5

 

[kingwinner]

But this is a "related rates" problem, so I believe that there should be more than 1 variable...but I can't figure out where and how to put in the second (or third) variable...

 

[Noober]

Let y be the distance from pulley to the angle opposite 15. Then you have x^2 + y^2 = 225, 2xdx + 2ydy = 0. Then plug in? Will that work?

 

[kingwinner]

But it says "At what speed is the box rising when the top of the box is 2 meters above the ground?", does it matter that it's 2 meters above? It is higher than the baseline of the triangle...

 

[2ltben]

Solve for dy/dt

 

[kingwinner]

I am quite lost...

If I let y to be the distance from pulley to the angle opposite 15, the box would be somewhere within the line, not at the bottom end of the line...

When the box is 2 meters above, it is higher than the baseline of the triangle...how can I use Pythagoras when the triangle is not fixed? This is the part that I really don't get...

Can anyone please help me? Thanks!