Register to reply

Related rates, baseball diamond

by rocomath
Tags: baseball, diamond, rates
Share this thread:
rocomath
#1
May23-08, 01:56 PM
rocomath's Avatar
P: 1,754
Even problem, very plz!

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 24 ft/s.

a) At what rate is his distance from second base decreasing when he is halfway to the first base?

b) At what rate is his distance from third base increasing at the same moment?

Work for A:

Distance from each base is x, evaluate when x = 45 ft

The distance from the runner to 2nd base, is z

Using Pythagorean theorem:

[tex]2x^2=z^2[/tex]

[tex]2x\frac{dx}{dt}=z\frac{dz}{dt}[/tex]

[tex]2x\frac{dx}{dt}=x\sqrt 2\frac{dz}{dt}[/tex]

[tex]\frac{dz}{dt}\approx -34.0 ft/s[/tex]

I'm mainly concerned with the set up, same for B?
Phys.Org News Partner Science news on Phys.org
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100
rootX
#2
May23-08, 03:50 PM
rootX's Avatar
P: 1,294
Quote Quote by rocomath View Post
Even problem, very plz!

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 24 ft/s.

a) At what rate is his distance from second base decreasing when he is halfway to the first base?

b) At what rate is his distance from third base increasing at the same moment?

Work for A:

Distance from each base is x, evaluate when x = 45 ft

The distance from the runner to 2nd base, is z

Using Pythagorean theorem:

[tex]2x^2=z^2[/tex]

[tex]2x\frac{dx}{dt}=z\frac{dz}{dt}[/tex]

[tex]2x\frac{dx}{dt}=x\sqrt 2\frac{dz}{dt}[/tex]

[tex]\frac{dz}{dt}\approx -34.0 ft/s[/tex]

I'm mainly concerned with the set up, same for B?
z = sqrt (90^2 + x^2)
z is your z
x is distance between him and first base

differentiate with respect to 't' .. don't know what you did

and same thing for the other base


Register to reply

Related Discussions
Related Rates Help please Calculus & Beyond Homework 9
Related Rates Calculus & Beyond Homework 5
Related Rates Calculus & Beyond Homework 5
Baseball related question Introductory Physics Homework 2
Related Rates Introductory Physics Homework 3