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?

aargh, did this yesterday, going to look


h^2 = 90^2 + x^2
h is hypotenuse
x is distance from third
where x = (4520t) 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 

x^2 = (4520*t)^2 + 90^2
2 x dx/dt = 2 *(4520t) (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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