Question

A baseball diamond is a square 90 ft on a side. A player runs from first base to second base at 10 ft/sec. At what rate is the player's distance from home base increasing when he is half way from first to second base?

Answer 1

Let the time after he leaves 1st base be t seconds
Then the distance he has gone at that time be 10t ft from first, and we have a right-angled triangle with legs of 10t ft and 90 ft
if the distance from the runner to home is d ft,
d^2 = 90^2 + (10t)^2 = 8100 + 100t^2
2d dd/dt = 200t
dd/dt = 100t/d

when he is halfway, 10t = 45
t = 4.5 , and d^2 = 8100 + 100(4.5)^2 = 10125
d = √10125 = 100.623 ft

dd/dt = 100(4.5)/100.623 = appr 4.47 ft/s

check my arithmetic

Answer 2

it didnt work out to be correct.

Answer 3

I checked the math

Answer 4

it had to have the square root in it still

Answer 5

geeeshh, then put the square root back in

dd/dt = 100(4.5)/√10125 ft/sec