Physical applications of calculus - Rates of change (1 Viewer)

[Aysce]

A lamp is 6m directly above a straight path. A man 2m tall walks along the path away from the light at a constant speed of 1m/s. At what speed is the end of his shadow moving along the path? At what speed is the length of his shadow increasing?

I've drawn the diagram correctly (I've checked the solutions) but I'm unsure of why you need to find: d(x+y)/dt for the first question?

 

[Sy123]

A lamp is 6m directly above a straight path. A man 2m tall walks along the path away from the light at a constant speed of 1m/s. At what speed is the end of his shadow moving along the path? At what speed is the length of his shadow increasing?

I've drawn the diagram correctly (I've checked the solutions) but I'm unsure of why you need to find: d(x+y)/dt for the first question?

My solution and diagram


If I am guessing the dimensions in your diagram correctly, x is the distance of the man from the pole, and y is the length of his shadow (or vice versa). So to find the rate at which the end of his shadow is moving will be d(y+x)/dt
We can easily label y+x=z as the whole thing but it doesnt really do anything so we just keep it as y+x.

My way was a little different to yours Im guessing since I had y as the whole length (doesnt make too much a difference in concept)