Part A
Suppose you are throwing a baseball. You release the ball with a perfectly horizontal velocity of 5.0 m/s at a height of 1.5 m above the ground. How far will the ball travel horizontally from the instant it leaves your hand until the instant it first contacts the ground?
System: The ball will be treated as a point particle subject to an influence from the earth (gravity).
Models: The ball is in projectile motion, so we model the x-component of the ball's motion as One-Dimensional Motion with Constant Velocity and the y-component as One-Dimensional Motion with Constant Acceleration.
Approach: The first thing to do is to sketch the situation, which allows us to summarize the givens and unknowns and also to set up a coordinate system.
In the problem statement, we are told that h = 1.5 m (as drawn in the picture) and we are asked for d. By drawing coordinate axes into our picture we have denoted the positive x and y directions. We have not yet chosen the origin, however (the axes can be placed wherever you wish on the picture to avoid clutter). We will take that step now. We choose our origin such that the position x = 0 m is the location at which the ball leaves the hand. The location y = 0 m is the level of the ground. With these choices made, we can summarize the givens (along with our traditional choice that ti = 0 s):
\begin
[ t_
= \mbox
] [ x_
= \mbox
][ x = d ] [ y_
= \mbox
] [ y = \mbox
][v_{x}} = \mbox
][v_{y,{\rm i}} = \mbox
] [ a_
= -\mbox
^
]\end
It is important to note that the phrase perfectly horizontal velocity of 5.0 m/s implies that the full velocity (5.0 m/s) is directed along the x-axis, with zero y-component for the initial velocity. This phrasing is extremely common in physics. You will also encounter the perpendicular case of a "perfectly vertical velocity". It is also worth remarking that although 5.0 m/s is the velocity at the instant of release (clearly the ball's initial velocity for the freefall trajectory of interest) we have written vx = 5.0 m/s rather than vx,i = 5.0 m/s. This is not a typo, because the x direction is subject to the 1-D Motion with Constant Velocity model (recall ax = 0). Because the x velocity is constant, it does not require labels for initial or final states.