Question

at what rate is his distance increasing from home plate when he is 35 feet from second base

Answer 1

The distance from the home plate is described by variable z. Then, the increasing rate is described by the derivative of z with respect to time, t.

Applying the Pythagorean theorem, the relation between z, x, and y is:

$\begin{gathered} z^2=x^2+y^2 \\ \text{Substituting with x = 55 ft and y = 90} \\ z^2=55^2+90^2 \\ z^2=3025+8100 \\ z=\sqrt[]{11125} \\ z=105.475116 \end{gathered}$

The derivative of x with respect to time is the speed of the player, that is,

$\begin{gathered} \frac{dx}{\differentialDt t}=22\text{ ft/s} \\ \end{gathered}$