I hope you had a good diagram.
1. A baseball diamond is a square with sides 90 ft. At the moment a batter hits the ball,
a runner from first base starts running to second base with a speed of 22 ft/sec
and a runner from second base starts running to third base with a speed of 28 ft/sec.
At what rate is the distance between these two runners changing 1 second later?
Is this distance increasing or decreasing?
D * * 90-x
o * B
* * x
* * A
At time , the runner on 1st has run feet from
. . where ft/sec. .Note that:
At the same time, the runner on 2nd has run feet from
. . where ft/sec.
Draw line segment , and let
Since is a right triangle: .
Differentiate with respect to time: .
. . and we have: . .
. . and: .
Substitute into : .