#4. Rain is falling at a velocity of 10,0 m/s at an angle of 30* towards the west. At what velocity and direction does a marathon runner have to go in order for him to get rain on his head?

To find the velocity and direction a marathon runner needs to go in order for him to get rain on his head, we can use vector addition.

First, let's break down the velocity of rain into its horizontal (westward) and vertical components.

Horizontal component (rain):
Velocity = 10.0 m/s * cos(30°)
= 10.0 m/s * √3/2
= 8.66 m/s (rounded to two decimal places)

Vertical component (rain):
Velocity = 10.0 m/s * sin(30°)
= 10.0 m/s * 1/2
= 5.00 m/s (rounded to two decimal places)

Now, for the marathon runner to get rain on their head, they need to have a vertical velocity component equal to the vertical component of the rain. In other words, the vertical velocities of the runner and the rain must be equal.

Thus, the marathon runner needs a vertical velocity of 5.00 m/s.

Next, let's determine the direction. Since the rain is falling towards the west, the runner needs to run towards the west with a speed that matches the horizontal component of the rain.

Therefore, the velocity and direction for the marathon runner to get rain on his head is:
Velocity = 8.66 m/s towards the west (horizontal component)
Velocity = 5.00 m/s upwards (vertical component)

Note: The above calculations assume that the rain falls directly downwards and there is no wind affecting the rain's velocity.