Question

Determine the magnitude of the horizontal component of the football’s initial velocity 0,v0,x, in terms of ℎvhorizontal, vvertical, g, and h.

A) v0,x=vhorizontal−g⋅h
B) v0,x=vhorizontal⋅g⋅h
C) v0,x=vhorizontal2−g⋅h
D) v0,x=gvhorizontal⋅h

Answer 1

The magnitude of the horizontal component of the football's initial velocity is equal to the horizontal velocity because there is no horizontal acceleration affecting it.

Step-by-step explanation:

The question asks to determine the magnitude of the horizontal component of the football's initial velocity (v0,x) in terms of the horizontal velocity (vhorizontal), vertical velocity (vvertical), acceleration due to gravity (g), and height (h). According to projectile motion principles in physics, the horizontal component of the velocity remains constant when there is no horizontal acceleration which is depicted as ax = 0 since horizontal motion is not affected by gravity. Therefore, we would not be subtracting or adding anything to vhorizontal related to gravitational pull or height.

With this in mind, it is clear that options A, B, and D that include gravity g and height h in their expressions to calculate v0,x are incorrect since these factors would only affect the vertical motion. Hence, we are left with the expression that keeps the horizontal velocity unchanged. So, the magnitude of the horizontal component of the football's initial velocity is simply the same as its horizontal velocity:

v0,x = vhorizontal.