Question

7. Katie and her best friend Liam play tennis every Saturday morning. When Katie serves the ball to Liam, it

travels 9.5 meters south in 2.1 seconds.
a.
What is the velocity of the tennis ball?
b. If the tennis ball travels at constant speed, what is its velocity when Liam returns Katie's serve?
​

Answer 1

Katie's serve has a velocity of approximately 4.52 m/s to the south. If Liam returns the serve at a constant speed, the velocity of the tennis ball is also 4.52 m/s but in the opposite direction, to the north.

Step-by-step explanation:

A: Velocity is defined as the displacement over time with direction. Given that Katie's serve travels 9.5 meters south in 2.1 seconds, we calculate the velocity by dividing the displacement by the time taken:

Velocity = Displacement / Time = 9.5 meters / 2.1 seconds ≈ 4.52 m/s to the south.

B: If the tennis ball travels at a constant speed when Liam returns Katie's serve, its velocity would be the same magnitude as Katie's serve but in the opposite direction (assuming a direct return). Hence, the velocity would be 4.52 m/s to the north.

Answer 2

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:

`v=(d)/(t)`

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:

`v=(9.5)/(2.1)=4.52 m/s`

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

`|v| = 4.52 m/s`

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