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: 1,756
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
Sapphire talk enlivens guesswork over iPhone 6
Geneticists offer clues to better rice, tomato crops
UConn makes 3-D copies of antique instrument parts
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