Question

A baseball diamond is a square with side 90
feet. If a batter hits the ball and runs towards
first base with a speed of 30 ft. per sec, at
what speed is his distance from second base
decreasing when he is half-way to first base?

Answer 1

set up a right angle triangle of lengths x,y,z
x=distance from runner to 1st
y=distance from 1st to 2nd
z=distance from runner to 2nd

so (z^2)(dz/dt) = (x^2)(dx/dt) + (y^2)(dy/dt)
(dz/dt) = [(45ft)^2 * (30ft/s) +(90ft)^2 * (0ft/s)] / (sqrt(45^2 + 90^2))^2
dz/dt = 6ft/s

Answer 2

where did you get 45ft form? Also how did you know to times it 30ft/s? How did you know to 90ft times zero ft/s? lastly how did you know to times 45ft times 90ft/s?

Answer 3

x is 45ft because that is the distance from the runner to first (90/2)
30ft/s comes from the rate of change in the x direction with respect to time
90 ft is multiplied by 0ft/s because there is no rate of change in the y direction ie. the runner is running perpendicular to the vector from 1st to 2nd
45 is never multiplied by 90, if what you are referring to is the last term in the calculation then it is just pythagorean theorem (z^2 = x^2 + y^2). z is calculated as the hypotenuse in the right angle triangle where x is 45 and y is 90

hope that helps.