Draw a velocity vector to represent the following (1cm represents 10km/h):
a) a girl running around a circular track travelling at 15km/h heading due east.
In the solutions, it shows it heading south, why is that?
To accurately represent the velocity vector for a girl running around a circular track, we need to consider both the speed and direction of her motion. In this case, the girl is traveling at 15 km/h, and the track is circular.
Since the track is circular, the girl's direction of motion is constantly changing. At any given point on the track, she is heading in a tangent direction to that point. Initially, when the girl starts running, she is heading due east. As she proceeds, her direction of motion changes continuously, always tangent to the circular path.
To determine the direction of the velocity vector, we can imagine drawing tangent lines to the circular path at different points. These tangent lines represent the instantaneous direction of motion at those points. It is important to note that the velocity vector is always tangent to the path at each point.
Since the girl's direction of motion changes as she runs around the circle, the velocity vector at any given point will be tangent to the circular path at that point. At the beginning, when she is heading due east, the tangent line will be horizontal, pointing eastward. As she moves, the direction of the tangent line will gradually change.
Now, let's consider why the solution shows the velocity vector heading south. As the girl runs around the circular track, the tangent line on one side will be pointing south, while the tangent line on the other side will be pointing north. This is because the circle is symmetric, and at one point, the girl has to be moving southward.
Therefore, when drawing the velocity vector to represent a girl running around a circular track at 15 km/h, heading due east, it is correct to show the vector pointing south at some point in the circular motion. This representation accurately reflects the changing direction of the girl's motion as she runs around the circular track.