Answer:
magnitude v0x = v0 * cos θ = 31 m/s * cos 16° = 30 m/s
Explanation:
Please see the figure for a graphical description of the problem. As you can see from the figure, the vector v0 (initial velocity) is the sum of its horizontal and vertical components v0x + v0y.
Using the trigonometric rule for right triangles:
cos θ = adjacent / hypotenuse
We can calculate the magnitude of the v0x vector.
Seeing the figure, notice that the vectors v0, its horizontal component, v0x, and its vertical component, v0y, form a right triangle.
v0x is the side adjacent to the angle θ, and v0 is the hypotenuse of the triangle. Then:
cos θ = magnitude v0x / magnitude v0
magnitude v0x = magnitude v0 * cos θ = 31 m/s * cos 16° = 30 m/s