Baseball diamond with a square side  ft.

Batter hits the ball and then runs towards the first base with a speed of 24 ft/s.

Draw diagram with the given specifications :

From the figure,

The man hits the ball at point and runs towards the point .

At any time , assume that man reaches some point , distance covered by him is ft .

and .

Speed of the man ft/s.

Assume the distance between the man and second base as at sec.

.

Since it is a square court, we have ft.

(a)

Apply Pythagorean theorem to the .

.

Substitute ,  and in above expression.

.

Differentiate on each side with respect to .

Here it is needed to determine at what rate is his distance from third base increasing when he is halfway to first base.

Thus, ft.

Substitute in .

Substitute , and   in .

Therefore, distance from second base decreasing at a rate  ft/sec. 

(b)

Apply Pythagorean theorem to the  .

.

Substitute ,  and in above expression.

.

Differentiate on each side with respect to .

Here it is needed to determine at what rate is his distance from second base decreasing when he is halfway to first base.

Thus, ft.

Substitute in .

Substitute , and in .

Therefore, distance from third base is increasing at a rate  ft/sec. 

(a) Distance from second base decreasing at a rate  ft/sec.

(b) Distance from third base is increasing at a rate  ft/sec.