Question

Assume that Clara and Mike run hard at 9 m/s under steady raindrop falling vertically to their head at 4 m/s.

a. At what angle raindrops hit their faces?
b. What is the speed of raindrops hitting their faces?

Answer 1

The angle at which raindrops hit their faces is approximately 24.4 degrees, and the speed of the raindrops hitting their faces is approximately 9.91 m/s.

Step-by-step explanation:

To find the angle at which the raindrops hit their faces, we can use trigonometry. Let's call the angle θ. Since the raindrops are falling vertically, the angle θ is the angle between their velocity vector and the vertical direction. We can find θ using the inverse tangent function:

θ = arctan(4 m/s / 9 m/s) = 24.4 degrees

To find the speed of the raindrops hitting their faces, we can use the Pythagorean theorem. The speed is the magnitude of the raindrop's velocity vector, which is the hypotenuse of a right triangle. We can use the velocity components of the raindrops and apply the Pythagorean theorem:

Speed = √((9 m/s)^2 + (4 m/s)^2) = 9.91 m/s