A dog stands at the beginning of an infinite flight of stairs, waiting for a man to shoot a ball up in the air.

A dog stands at the beginning of an infinite flight of stairs, waiting for a man to shoot a ball up in the air. If he can climb one set of stairs every 3 s, each 10 m tall, the man shoots the ball with a velocity of 250 m/s. How many sets of stairs can he climb before has to lean out the window to catch the ball? What will the speed of the ball be when he catches it?