Related rates, baseball diamond

  • Thread starter rocomath
  • Start date
  • #1
rocomath
1,755
1
Even problem, very please!

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?
 

Answers and Replies

  • #2
rootX
465
4
Even problem, very please!

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
 

Suggested for: Related rates, baseball diamond

Replies
1
Views
687
  • Last Post
Replies
19
Views
1K
  • Last Post
Replies
3
Views
953
Replies
30
Views
2K
  • Last Post
Replies
11
Views
976
Replies
13
Views
686
  • Last Post
Replies
3
Views
1K
Replies
22
Views
2K
Replies
2
Views
284
  • Last Post
Replies
3
Views
2K
Top