Problems, about instantaneous variation rates.

Problem 1

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 24 ft/s.

a) At what rate is his distance from second base decreasing when he is halfway to first base?

b) At what rate is his distance from third base increasing at the same moment?

 Problem 2

The radius of a sphere is increasing at a rate of 4mm/s.  How fast is the volume increasing when the diameter is 80 mm?

 Problem 3

The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s.  When the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing?

 Problem 4

Two people start from the same point.  One walks east at 3 mi/h and the other walks northeast at 2 mi/h. How fast is the distance between the people changing after 15 minutes.