A baseball is moving along the third base line at a constant velocity of 100 feet per second. If a baseball diamond is a 90-foot square, then how quickly is the distance from the ball to first base changing when:
- the ball is halfway to third base;
- the ball is at third base.
First, we give the general set up for the problem.
The following diagram illustrates the situation:
The quantity we are given then is
Further, ; thus, and so
Now, the two requested cases:
- If the ball is halfway to third base, this means feet (since the diamond is a square with sides of length 90 feet). So we have,
- If the ball is at third base, this means (since is the distance from the ball to home plate), thus we have,