Question

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

At what rate is his distance from second base changing when he is halfway to first base?

At what rate is his distance from third base changing at the same moment?

Answer 1

think of distance from 2nd base as the hypotenuse of a right triangle
where other 2 sides are 90 and (90-x) where x is distance runner has run

Answer 2

\[D = \sqrt{90^{2} + (90-x)^{2}}\]
find rate this is changing, then multiply by speed of runner dx/dt
\[\frac{dD}{dt} = \frac{dD}{dx}*\frac{dx}{dt}\]

Answer 3

what do you mean find rate this is changing?

Answer 4

sorry i mean take derivative