Calculus Question

Question

Two people start from the same point. One walks east at 3 mi/h and the other walks northeast at 5 mi/h. How fast is the distance between the people changing after 15 minutes? (Round your answer to three decimal places.)

Answer 1

Make a drawing; from the starting point, draw an horizontal line segment labeled 3t (that's the distance covered in t hours). Draw another line segment labeled 5t, in the NE direction from the starting point; this will form a 45 degree angle with the eastbound traveler.

 

You now connect the endpoints of the two line segments and label it z.

 

Use the Law of Cosines to express z² and use this as the basis for finding dz/dt, in general.

When t = ¼ hr, calculate the specific dz/dt.