Can anyone help
A baseball diamond has the shape of a square with sides 90 feet long. A player 30 feet from third base is running at a speed of 28 feet per second. At what rate is the player’s distance s from the home plate?
With that assumption, imagine, or draw the figure on paper. It is a right triangle, with these:
---one leg = x ---------the portion of 2nd-to-3rd-base side, from the 3rd base.
---other leg = 90 ft ----the 3rd-to-home-base side.
---hypotenuse = s -----distance from runner to the home base.
By Pythagorean theorem,
s^2 = x^2 +90^2
Differentiate both sides with respect to time t,
2s(ds/dt) = 2x(dx/dt)
s(ds/dt) = x(dx/dt) ------------(1)
Now, in (1) we know that:
dx/dt = -28 ft/sec ----negative because x is getting shorter with time t.
x = 30 ft
We are looking for ds/dt.
But we do not know the s. So we find the s at that instant.
When x=30 ft,
s^2 = 30^2 +90^2
s^2 = 9000
s = 30sqrt(10)
So, plug those into (1),
[30sqr(10)](ds/dt) = 30(-28)
ds/dt = -28/sqrt(10)
ds/dt = -8.854 ft/sec ----negative, so s is getting shorter with time also.
Therefore, the distance of the player from the home base at that instant is decreasing at the rate of 8.854 ft/sec. ---------answer.