During a baseball game a fly ball is hit to center field and is caught 121 m from home plate. Just when the ball is caught, a runner on third base takes off for home, and the center fielder throws the ball to the catcher standing on home plate. The runner takes 3.00 s to reach home, while the baseball is thrown with a velocity whose horizontal component is 43 m/s. Which reaches home first, the runner or the ball, and by how much time?

Question

anonymous · Answer

First, you need to find how long it takes for the ball to travel 121m.  Do

$$d/v_x = t = 121/43$$

Now look at that time, and compare it to the runner's time.

There is a subtlety here.  I am assuming, as I think the problem is also assuming, that the ball travels in a straight line path.  However, in reality, the ball is subject to gravity and will thus travel a parabolic path.  In parabolic motion, the time to reach home depends on how high the ball is thrown.  Think about it.  If the ball is thrown high, it'll take longer than if he throws a line-drive towards home.  So, what we calculated here is actually the shortest amount of time that the ball could reach home.  If you a currently studying parabolic motion, you may need to reread the problem.  Typically, you'll need parabolic motion type stuff if there is an angle of elevation in the problem.  There is none here.