Question

A baseball diamond is a square with each side 90 feet in length. A player take an aggressive turn around second and realizes he must return. Therefore, he is running from third base back to second base at a rate of 10 f/s. At what rate is angle a decreasing when D is 18 feet? Round your answer to 3 decimal places or answer as a reduced fraction.

Answer 1

The rate of change of angle a when D, is 18 feet is 0.0114 radians per second.

Baseball diamond side length (a)= 90 ft

Player's running rate (v)= 10 ft/s

Distance from player to second base = 18 ft

We can use the right triangle formed by the player's position (D), second base (S), and home plate (H) to relate the variables:

tan(θ) =
`(d)/(a)`