Question

At what angle, in degrees, to vertical do the raindrops move as measured by an observer in the car?

Answer 1

Using vector addition and trigonometry, the raindrops moving at 4.5 m/s appear to the observer in a car moving at 22.0 m/s to be at an angle of approximately 11.59 degrees to the vertical.

Step-by-step explanation:

The scenario presented is a physics problem where an observer in a moving vehicle observes raindrops. To calculate the angle to vertical at which the raindrops appear to move relative to the observer in the car, one must use vector addition to combine the velocity of the raindrops with the velocity of the car. The raindrops fall vertically at 4.5 m/s, and the car moves horizontally at 22.0 m/s. The resultant velocity of the raindrops as seen by the observer can be found using the Pythagorean theorem, and the angle can be obtained using the inverse tangent function (tan-1(vertical/horizontal)).

To find the angle, we calculate:

Angle to vertical = tan-1(raindrop velocity / car velocity)

Angle to vertical = tan-1(4.5 m/s / 22.0 m/s)

Angle to vertical = tan-1(0.2045)

Angle to vertical ≈ 11.59°

Therefore, the observer in the car sees the raindrops moving at an angle of approximately 11.59° to the vertical.