Posted by **Shawn** on Thursday, December 30, 2010 at 3:51pm.

A baseball player hits a line drive to center field. He runs from second to third at 20 feet/sec. How fast is the distance from the runner to home plate changing when he is halfway to third base?

- Calculus -
**Reiny**, Thursday, December 30, 2010 at 5:45pm
If I recall, the length of a side of a baseball diamond is 90 feet.

Make a diagram of a right-angled triangle using the third base line as one side, the distance of the runner to home plate as the hypotenuse h, and letting the distance of the runner to third be x feet

then x^2 + 90^2 = h^2

2x dx/dt = 2h dh/dt

dx/dt = h (dh/dt) / x

we know dx/dt = -20 ft/sec

and when x= 45

h^2 = 45^2 + 90^2

h = √10125

dh/dt = √10125(-20)/45 = .....

(the negative value of dx/dt shows that the value of x is decreasing, as I defined x)

## Answer this Question

## Related Questions

- math - A baseball player hits a line drive to center field. As he rounds second ...
- Calculus - As a baseball player runs from second to third base, he is going 20 ...
- Calculus - A baseball diamond is a 90 foot square with the pitcher's mound at ...
- Calculus - A Baseball Diamond has the shape of a square with sides 90 feet long...
- math/physics - During a race, one runner runs at a 6 min/mi pace and another ...
- Math (trig) - The distance from home plate to dead center field in a certain ...
- math - 1. A baseball diamond is a square with a distance of 90 feet between the ...
- physics - A baseball player hits a home run over the left-field fence, which is ...
- math - a baseball player hits sa pitch when the ball is 2 feet off the ground. ...
- Math - A baseball player hits a pitch when the ball is 2 feet off the ground. ...

More Related Questions