Question

During a baseball game, a baseball is struck at ground level by a batter. The ball leaves the baseball bat with an initial velocity v0 = 31 m/s at an angle θ = 16° above horizontal. Let the origin of the Cartesian coordinate system be the ball's position the instant it leaves the bat. Air resistance may be ignored throughout this problem. Express the magnitude of the ball's initial horizontal velocity v0x in terms of vo and θ.

Answer 1

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