Question

A baseball diamond is a square with sides of length 90 ft. Assume Edgar hits a home run and races around the bases (counterclockwise) at a speed of 9 ft/sec.
Express the distance between Edgar and home plate as a function of time t. (Hint: This will be a multipart function.)

Answer 1

Answer:

i) In the interval 0 ≤ t ≤ 10

   d(t)  = 9t

ii) In the interval 10 ≤ t ≤ 20

    d(t) =$\sqrt{\{9(t - 10)\}^{2} + 90^{2} }$ =  $9\sqrt{(t - 10)^{2} + 10^{2} }$

iii) In the interval 20 ≤ t ≤ 30

  d(t)  = $9\sqrt{(30-t)^{2} + 100}$

iv) In the final interval 30 ≤ t ≤ 40

  d(t) = 360 - 9t

Step-by-step explanation:

Let d(t) be the function of the distance between Edgar and home plate as a function of time.

Edgar takes $= \frac{90feet}{9feet\hspace{0.1cm}s^{-1} } = 10 seconds$ to run each side of the baseball diamond.

i) In the interval 0 ≤ t ≤ 10

   d(t)  = 9t

ii) In the interval 10 ≤ t ≤ 20

    d(t) =$\sqrt{\{9(t - 10)\}^{2} + 90^{2} }$ =  $9\sqrt{(t - 10)^{2} + 10^{2} }$

iii) In the interval 20 ≤ t ≤ 30

  d(t)  = $9\sqrt{(30-t)^{2} + 100}$

iv) In the final interval 30 ≤ t ≤ 40

  d(t) = 360 - 9t