Explain why the potential differences across each bulb do not add to the battery’s voltage, when the switch is closed.

This is due to the gap in between the switch. So the applied energy is not converted to current even though the resistance is still there. Hence voltage will be there, where you applied it

Explanation:

We are given:

Direction of motion: 25 degrees south of the east axis

Distance covered  = 125 m

East component of the Ball:

this component is denoted by green color in the image

Once we drop a perpendicular from the end of the direction vector on the x-axis, we get a right angled triangle

The magnitude of the side of the triangle on the x-axis denotes the east component of the ball

Using trigonometry, we find that the east component of the ball is:

125 * Cos(25 degrees)

125 * 0.9 = 112.5 i   (here, i denotes rightward direction on the x-axis)

North Component of the Ball:

this component is denoted by blue color in the image

Using trigonometry, we find that the North component of the ball is:

125* Sin(25 degrees)  (-j)      [j denotes upward movement on the y-axis, since the vector is acting downwards, we have used '-j']

125 * 0.42 (-j)

52.5 (-j) =   -52.5 j

Therefore the direction vector of the ball is 112.5 i - 52.5 j

where 112.5 i is the East Component and -52.5 is the North Component