The first formula we shall consider concerns the vertical motion of a ball thrown up in the air. From Newton's second law of motion one can set up a mathematical model for the motion of the ball and find that the vertical position of the ball, called y, varies with time t according to the following formula: y(t)=v0t21gt2. Here, v0 is the initial velocity of the ball, g is the acceleration of gravity, and t is time. Observe that the y axis is chosen such that the ball starts at y=0 when t=0. The above formula neglects air resistance, which is usually small unless v0 is large, see Exercise 1.11. To get an overview of the time it takes for the ball to move upwards and return to y=0 again, we can look for solutions to the equation y=0 v0t21gt2=t(v021gt)=0t=0ort=2v0/g. That is, the ball returns after 2v0/g seconds, and it is therefore reasonable to restrict the interest of (1.1) to t[0,2v0/g]