A small cart is rolling at constant velocity vo on a flat track. As it continues to move, a launcher, fixed onto the cart, fires a marble straight up into the air when the end of the launching barrel is passing point
i, as shown in the figure. If the launching barrel reaches the position of point ii when the marble returns
to the same vertical position that it was launched from, what will be its horizontal position? (Assume air
resistance is neglible)

You have two photos of a person walking. one shows the person at the corner of third and main streets, the other shows the person at the corner of tenth and main streets. there are lampposts at every corner in this town, and the first picture shows it to be 10: 32: 00 exactly. the second picture shows it to be 10: 49: 30. you know three facts: (1) all of the clocks are synchronized; (2) there are exactly 12 equal-sized blocks per kilometer in this town; and (3) the streets that cross main in this area are numbered consecutively, with no interruptions. what is the person’s average speed in kilometers per hour?