A baseball diamond is a square 90 ft on a side. A player runs from first base to second at a rate of 16 ft/sec.

a. At what rate is the player’s distance from third base changing when the player is 30 ft from first base?

b. At what rates are angles θ₁ and θ₂ (see the figure) changing at that time?

c. The player slides into second base at the rate of 15 ft/sec. At what rates are angles θ₁ and θ₂ changing as the player touches base?

Third base 90' 0 Second base 0 Home Player 30' First base