Direction for Holding Umbrella at Bus Stop:

To determine the direction in which the boy waiting at the bus stop should hold his umbrella, we need to consider the combined effect of rain falling vertically and the wind blowing horizontally.

1. Rain Falling Vertically:
The rain is falling vertically with a speed of 35 m/s. This means that the raindrops are coming straight down from the sky.

2. Wind Blowing East to West:
The wind starts blowing after some time with a speed of 12 m/s in the east to west direction. This means that the wind is moving horizontally from east to west.

Combined Effect of Rain and Wind:
When the wind blows, it affects the path of the raindrops. The raindrops will not fall straight down, but will be deflected in the direction of the wind. The magnitude of deflection depends on the speed of the wind.

In this case, the wind is blowing from east to west, which means it is perpendicular to the direction in which the rain is falling. As a result, the raindrops will be deflected towards the west.

Direction to Hold the Umbrella:
To protect himself from the rain, the boy should hold his umbrella in the direction opposite to the deflection caused by the wind. In this case, since the raindrops are deflected towards the west due to the wind blowing from east to west, the boy should hold his umbrella in the eastward direction.

Therefore, the boy waiting at the bus stop should hold his umbrella in the eastward direction to protect himself from the rain. This will ensure that the umbrella covers him effectively and prevents the rain from reaching him.

Summary:
- Rain is falling vertically with a speed of 35 m/s.
- Wind starts blowing from east to west with a speed of 12 m/s.
- The wind deflects the raindrops in the direction of the wind, which in this case is towards the west.
- The boy should hold his umbrella in the eastward direction to protect himself from the rain effectively.