a. 4.52 m/s south
Velocity is a vector, whose magnitude is defined as the ratio between the displacement of the object and the time taken for the displacement to occur:
[tex]v=\frac{d}{t}[/tex]
where
d is the displacement
t is the time
Velocity is a vector, so it also has a direction, which corresponds to that of the displacement.
For the ball in this problem,
d = 9.5 m south
t = 2.1 s
Substituting, we find:
[tex]v=\frac{9.5}{2.1}=4.52 m/s[/tex]
and the directiion is the same as the displacement (south).
b. 4.52 m/s north
For this part, we must keep in mind that the speed is the magnitude of the velocity; however, speed is a scalar, so it does not have a direction.
Here we are told that the tennis ball travels at constant speed, so on its way back from Liam to Katie the ball's velocity is still the same as before, therefore
[tex]|v| = 4.52 m/s[/tex]
However, this time the direction is opposite to before, since the ball is travelling in the opposite direction.
Therefore, the ball's velocity when Liam returns Katie's service is
4.52 m/s north
