SOLUTION: A baseball diamond is a square with side 90ft. a batter hits the ball and runs toward first base with a speed of 26 ft/sec. At what rate is his distance from second base decreasing

Question 409281: A baseball diamond is a square with side 90ft. a batter hits the ball and runs toward first base with a speed of 26 ft/sec. At what rate is his distance from second base decreasing when he is halfway to first base?
I keep getting the answer -10.7ft/sec, but the correct answer that was given was 11.6ft/sec...I dont understand what I'm doing wrong?!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
A baseball diamond is a square with side 90ft. a batter hits the ball and runs toward first base with a speed of 26 ft/sec. At what rate is his distance from second base decreasing when he is halfway to first base
..
let z=runner's distance from second base
x=runner's distance from first base
dx/dt= runner's speed
z^2=90^2+x^2
differentiate both sides with respect to time, t
2z(dz/dt)=0+2x(dx/dt)
z(dz/dt)=x(26 ft/sec)
when runner is half way to first base, z=sqrt(90^2+45^2)=100.623
dz/dt=(45*26)/100.623=11.62 ft/sec
ans:
When runner is half way to first base, his distance to second base is decreasing at a rate of 11.62 ft/sec
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