A river 100 ft wide is flowing north at w feet per second. A dog starts at (100, 0) and swims at v₀ = 4 ft/s, always heading toward a tree at (0, 0) on the west bank directly across from the dog’s starting point.

(a) If w = 2 ft/s, show that the dog reaches the tree.

(b) If w = 4 ft/s, show that the dog reaches instead the point on the west bank 50 ft north of the tree.

(c) If w = 6 ft/s, show that the dog never reaches the west bank.