# Related Rates Questions:

1. Apr 25, 2005

### scorpa

Hello,

I'm having some troubles with some more rates questions and was wondering if someone could help me out.

A construction worker pulls a 5m plank up the side of a building under construction by means of a rope tied to the end of a plank. The opposite end of the plank is being dragged along the ground. If the worker is pulling at a rate of 15 cm/s, how fast is the end of the plank sliding along the ground when it is 2m from the wall of the building?

A fish is being reeled in at a rate of 30cm/s from a bridge 4m above water. At what rate is the angle (in rad/s) between the line and the water chaning when there is 8m of line out?

The relation between distance s and velocity v is given by v = 150s/(3+s). Find acceleration in terms of s.

I had no clue how to do the first two, but I thought I could do the second so I found the first and second derivative of the equation thinking that it would give me the answer but it did not, so I guess I am more lost than I though. Any help would be greatly appreciated.

2. Apr 25, 2005

### whozum

You only need to use the chain rule and the first derivative, theres no need for third derivatives in the fisrt two. Try to come up with equations relating the distance from the ladder base to the wall, the angle theta, and the height the ladder reaches. Drawing a triangle is very helpful

For the last however, use the relationship

$$a = \frac{dv}{dt}$$