Question

arrow showing his sideways speed. click play, click throw, and then click pause. notice there are now three arrows coming from the ball.
a. what do you think the blue arrow represents? ​the train’s forward motion (speed of the train).
b. what do you think the red arrow represents? ​the sideways motion of the thrower relative to the train.
c. what do you think the yellow arrow represents? ​the total velocity of the ball (combination of throw + train motion)

1. experiment. try different combinations of thrower speed and throw speed.

a. how does the throw speed (blue arrow) affect the ball velocity (yellow arrow)? ​blank
b. how does the thrower velocity (red arrow) affect the ball velocity (yellow arrow)? ​blank

Explanation:

4A

The blue arrow represents the train's forward speed (throw speed here, maybe a typo for train speed). In velocity addition (vector addition), the throw speed (train's forward speed) is one component of the ball's total velocity (yellow arrow). As the throw speed (blue arrow magnitude) increases, the magnitude of the yellow arrow (total velocity) in the forward direction increases. Since velocity is a vector, the forward component from the blue arrow contributes to the total velocity vector (yellow). So increasing the throw speed (blue) increases the yellow arrow's magnitude in the forward direction, thus increasing the total ball velocity (yellow) if we consider the forward component's contribution.

The red arrow represents the thrower’s sideways velocity relative to the train. The total velocity of the ball (yellow arrow) is the vector sum of the train’s forward velocity (blue) and the thrower’s sideways velocity (red). So, as the thrower’s velocity (red arrow magnitude) increases, the magnitude of the sideways component of the ball’s total velocity increases. Since the total velocity is the vector combination of the forward (blue) and sideways (red) velocities, an increase in the red arrow’s magnitude will increase the magnitude of the yellow arrow (total velocity) because the sideways component contributes more to the resultant vector. Also, the direction of the yellow arrow will shift more towards the sideways direction (the direction of the red arrow) as the red arrow’s magnitude increases relative to the blue arrow’s magnitude.

Answer:

As the throw speed (blue arrow, representing the train’s forward speed) increases, the magnitude of the ball’s total velocity (yellow arrow) in the forward direction increases. Since the total velocity is the vector sum of the train’s forward motion (blue) and the thrower’s sideways motion (red), a greater forward speed (blue) adds more to the forward component of the total velocity, resulting in a larger - magnitude yellow arrow (total velocity) in the direction that combines both motions.

4B