# math

posted by stephen

A baseball player hits a line drive to center field. As he rounds second base, he heads directly for third, running at 20 ft/sec. How fast is the distance from the rnner to home plate changing when he is halfway to third base?

1. Damon

aargh, did this yesterday, going to look

2. bobpursley

3. Damon

h^2 = 90^2 + x^2
h is hypotenuse
x is distance from third
where x = (45-20t) so dx/dt = -20

2 h dh/dt = 2 x dx/dt
dh/dt = (x/h) (-20)
at t = 0, x = 45 and h = 100.6
so
dh/dt = -8.94

4. Damon

http://www.jiskha.com/display.cgi?id=1293827209

5. Damon

x^2 = (45-20*t)^2 + 90^2
2 x dx/dt = 2 *(45-20t) (-20)
at x=sqrt(45^2+90^2) when t = 0
2 (100.6) dx/dt = 90*-20
dx/dt = -8.94 ft/s

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