A hare and a tortoise compete in a race over a course 2.80 km long. The tortoise crawls straight and steadily at its maximum speed of 0.700 m/s toward the finish line. The hare runs at its maximum speed of 6.00 m/s toward the goal for 0.800 km and then stops to tease the tortoise. How close to the goal can the hare let the tortoise approach before resuming the race, which the tortoise wins in a photo finish? Assume that, when moving, both animals move steadily at their respective maximum speeds.

A child plays on an escalator by going up and down while the escalator is moving. When he runs upward in the same direction with the escalator he can reach the upper level in 27 seconds. Then he runs downward in the opposite direction of the escalator, and he reaches the lower level in 79 seconds. The child has the same average speed relative to the escalator in both cases. If the speed of the escalator is 1.58 m/s, calculate the speed of the child. Please use m/s unit for the answer. Thank you

A juggler throws a bowling pin straight up with an initial speed of 9.7 m/s from an initial height of 2.8 m. How much time elapses until the bowling pin returns to the same initial height?

A runner and a cyclist compete in a race over a straight course 20 km long. The runner runs at a steady speed of 10 m/s toward the finish line. The cyclist zips at a speed of 23 m/s toward the finish line for 12 km but upon seeing that he is already far ahead of the runner, he decides to stop and wait for the runner to catch up to him. The runner eventually reaches the cyclist and continues moving toward the finish line. The cyclist waits for a while after the runner passes and then cycles toward the finish line again at 23m/s.    Both the cyclist and the runner cross the finish line in the exact same instant. Assume both of them, when moving, move steadily at their respective speeds.  (a) How far is the runner from the finish line when the cyclist resumes the race?  (b) For how long in time was the cyclist stationery?