Question

MEDAL!!!
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 20 ft/s.

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

I know i must take the derivative of the equation to find the rate of change, I just do not know how to set the equation up. The more details I can get on this the better it would help me, Thank You!!

Answer 1

You have to start by figuring out how far away he is from second base at two points, say from halfway to first and when he reaches first. Having those two points will enable you to derive the equation.

Answer 2

see the picture for the definitions

from pythagoras
\[ 90^2 + y^2= x^2 \\
\frac{d}{dt} \left( 90^2 + y^2= x^2\right)\\
2y \frac{dy}{dt} = 2 x \frac{dx}{dt} \\
y \frac{dy}{dt} = x \frac{dx}{dt}
\]

now fill in for dy/dt, y , and x
\[ x= \sqrt{45^2 +90^2} \]