1.) At time , we may state:

Implicitly differentiating with respect to , and solve for

We are given the conditions:

So, use these to find the value of , which represents the vertical speed of the balloon at the given point.

2.) Let x be the distance of the base of the ladder from the wall and y be the height of the top of the ladder on the wall. We may then relate the angle of elevation to these variables with

(1)

We also know by Pythagoras that:

(2)

Differentiate (1) with respect to and solve for , and replace the resulting trig. function by its ratio definition.

Differentiate (2) with respect to to find .

Now, you should have everything you need to answer the question.