1. The problem statement, all variables and given/known data A wildebeest is charging across a plain. His path takes him to location (x,y) where x is his distance (in miles) east of his starting point and y is his distance in miles north of his starting point at time t. So x and y are functions of t. The air temperature is a function of both location and time. Right now he is moving at a velocity of 12 miles per hour in the northward direction and 7 miles per hour westward. In the northward direction the temperature changes at a rate of -0.10 degrees per mile, and in the eastward direction the temperature changes at a rate of -0.05 degrees per mile. Also, overall the temperature (irrespective of location) is changing at a rate of -1.6 degrees per hour. What is the rate of change in air temperature that the wildebeest is experiencing right now? 3. The attempt at a solution I just want to make sure I set this up right. I first created a function called r(t). We then have [itex] ∇r = -7 i + 12 j + 1 k [/itex] Next I made a unit vector for the 3 respective changes in temperature [itex] u = -.05/1.603)i - .1/1.603) j + 1.6/1.63 k [/itex] Next I just summed the dot product [itex] ∇r * u [/itex] I just wanted to make sure there are no errors in this solution, and that I set it up in an efficient manner. I have trouble when I have to start mixing (x,y) with t. Thank you.