Answer:
d(L)/dt = 6,96 ft/s
Explanation:
We have a right triangle where the hypotenuse (L) is the distance between the player and home plate, the legs are the line between third base and home plate ( 90 feet ) and distance between the player and third base (x) (over the line between second and third base). So we can write
L² = (90)² + x²
Applying differentiation in relation to time, on both sides of the equation we have:
2*LdL/dt = 0 + 2*x d(x)/dt (2)
In this equation we know:
d(x)/ dt = 22 feet/sec
x = 30 ft
We need to calculate L when the player is at 30 feet from third base
Then
L² = (90)² + (30)²
L² = 8100 + 900
L = √9000
L =94,87 feet
Then we are in condition for calculate d(L)/dt from the equation
2*Ld(L)/dt = 0 + 2*x d(x)/dt
2*94,87 * d(L)/dt = 2* 30* 22 ⇒ 189,74 d(L)/dt = 1320
d(L)/dt = 1320/ 189,74
d(L)/dt = 6,96 ft/s
