How do you determine the direction of the initial velocity from a y vs x graph?

 

Imagine watching a friend throw a ball to another friend as shown in the diagram below.� Because of gravity, the ball doesn�t follow a straight line.� In fact, if the drag force from air can be ignored, then the ball follows a path that is shaped like a parabola.� This parabolic path is called the �trajectory� of the ball.�

 

 

Now compare the trajectory in the diagram above to the y vs x graph for the same ball that is shown below.�

 

 

They appear to be identical because they are.� Both represent a plot of the vertical coordinate y vs the horizontal coordinate x of the ball.� In short, a y vs x graph of a motion is identical to the trajectory in a photograph of that motion.�

 

The diagram below is identical to the one above, but this time, the ball is shown at five different instants as it moves along its trajectory.� A velocity vector has also been drawn at each of these five instants.� The directions of these velocity vectors indicate the direction the ball is moving at each instant.� Notice that each of the velocity vector is tangent to the trajectory.�

 

 

The reason you chose to read this blurb of text is to answer the question:

�������� �How do you determine the direction of the initial velocity?�

 

The initial velocity has the same direction as the vector that is tangent to the trajectory at the initial location of the ball!� In the diagram above, the initial location is the instant the ball leaves the person�s hand.� Hence, the vector labeled �v₀� in the diagram is the initial velocity.� In the simulation, the initial location is indicated by the data point that has a black border and is slightly larger than the other data points.� Hence, to determine the direction of the initial velocity, simply determine the direction that is tangent to the trajectory at that point.�