Snow is falling vertically at a constant rate of 8.0 m/s. At what angle from the vertical do the snowflakes appear to be falling as viewed by the driver of a car traveling on a straight, level road with a speed of 50k.h?
To determine the angle at which the snowflakes appear to be falling as viewed by the car driver, we can use trigonometry and the concept of relative motion.
Let's consider the situation from the car driver's perspective. The snowflakes are falling vertically at a constant rate of 8.0 m/s. However, due to the car's velocity, the snowflakes will also appear to have a horizontal component of motion.
The car is traveling on a straight, level road with a speed of 50 km/h. Before proceeding, we need to convert this speed to meters per second (m/s) since the rate of snowfall is given in meters per second.
1 km/h is equal to (1000/3600) m/s, so 50 km/h is equal to (50 * 1000/3600) m/s, which is approximately 13.9 m/s.
Now, let's break down the motion of the snowflakes into vertical and horizontal components:
Vertical Component: The vertical component of the snowflake's motion is simply 8.0 m/s, as stated in the question.
Horizontal Component: The horizontal component is equal to the car's velocity, which is 13.9 m/s.
To find the angle at which the snowflakes appear to be falling, we can use the tangent of the angle. The tangent of an angle is the ratio of the opposite side to the adjacent side in a right triangle.
Tangent (θ) = Opposite/Adjacent
In this case, the opposite side is the vertical component of the snowflake's motion, and the adjacent side is the horizontal component. So we have:
Tangent (θ) = 8.0 m/s / 13.9 m/s
θ = arctan(8.0/13.9)
Using a calculator or a trigonometric table, we find that θ is approximately 29.2 degrees.
Therefore, the snowflakes appear to be falling at an angle of approximately 29.2 degrees from the vertical as viewed by the car driver.