The picture above shows a football player kicking a football. this is known as two dimensional motion. in which direction does the football move? a) vertical only (y) b) horizontal only (x) c) horizontal and vertical (x, y) d) horizontal, vertical, and side to side (x, y, and z) the diagram shows the motion of a tennis ball that has just been hit with a racket (air resistance is neglected). which of these is true of the horizontal and vertical components of the ball’s velocity? a) both the horizontal and the vertical components are constant. b) both the horizontal and the vertical components are accelerated. c) the horizontal component is constant but the vertical component is accelerated. d) the horizontal component is accelerated but the vertical component is constant.

1. C)horizontal and vertical (x, y)

The picture shows the motion of a projectile, which consists of two separate motions along two different directions:

- horizontal (x): along this direction, the football has a uniform motion, with constant horizontal speed ,where is the magnitude of the initial velocity of the ball and the angle at which it has been thrown

- vertical (y): along this direction, the football has an accelerated motion, with initial vertical velocity upward and constant acceleration downward (acceleration due to gravity)

2. C)The horizontal component is constant but the vertical component is accelerated.

As described in the previous part of the exercise:

- along the horizontal direction there are no forces exerted on the ball, so it is a uniform motion, therefore the acceleration is zero and the horizontal component of the velocity is constant

- along the vertical direction there is one force acting on the ball (the force of gravity, which pushes downward), so there is an acceleration (downward) equals to and therefore the vertical component of the velocity is not constant.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.