Motion in the horizontal direction does not affect motion in the vertical direction, and vice versa.
If you can, download this PhET Interactive Simulation. Learn about position, velocity and acceleration vectors. We will find such techniques to be useful in many areas of physics.
We shall see how to resolve vectors in the next couple of lessons. Resolving two-dimensional motion into perpendicular components is possible because the components are independent. The key to analyzing such motion, called projectile motion, is to resolve (break) it into motions along perpendicular directions. The two-dimensional curved path of the horizontally thrown ball is composed of two independent one-dimensional motions (horizontal and vertical). In the real world, air resistance will affect the speed of the balls in both directions. Note that this case is true only for ideal conditions. This result means that the horizontal velocity is constant, and affected neither by vertical motion nor by gravity (which is vertical). This is due to the fact that there are no additional forces on the ball in the horizontal direction after it is thrown. (Assuming no air resistance, the vertical motion of a falling object is influenced by gravity only, and not by any horizontal forces.)Ĭareful examination of the ball thrown horizontally shows that it travels the same horizontal distance between flashes. This similarity implies that the vertical motion is independent of whether or not the ball is moving horizontally. In the middle case, when the vectors are perpendicular, the dot product will be 0.2 On the far. It is remarkable that for each flash of the strobe, the vertical positions of the two balls are the same. So if we take the dot product of a vector with itself, we.
This shows that the vertical and horizontal motions are independent. Despite the difference in horizontal velocities, the vertical velocities and positions are identical for both balls. The ball on the right has an initial horizontal velocity, while the ball on the left has no horizontal velocity. Arrows represent horizontal and vertical velocities at each position. Each subsequent position is an equal time interval. This shows the motions of two identical balls-one falls from rest, the other has an initial horizontal velocity.