# Oblique movement

An oblique motion is a part vertical and part horizontal movement. For example, the movement of a stone being thrown at a certain angle with the horizontal, or a ball being kicked at an angle with the horizontal.

With the fundamentals of vertical movement, it is known that when air resistance is neglected, the body only undergoes gravity acceleration.

## Oblique or Projectile Throw

The furniture will move forward on a path that goes to a maximum height and then descends again, forming a parabolic path. To study this movement, oblique motion must be considered to be the resultant between vertical motion (y) and horizontal movement (x).

In the vertical direction the body performs a Evenly Varied Movement, with initial velocity equal to and acceleration of gravity (g)

In the horizontal direction the body performs a uniform movement with velocity equal to .

• During ascent the vertical speed decreases, it reaches a point (maximum height) where , and goes down increasing the speed.
• The maximum range is the distance between the point of release and the point of fall of the body, ie where y = 0.
• The instantaneous velocity is given by the vector sum of the horizontal and vertical velocities, that is, . The velocity vector is tangent to the trajectory at each moment.

Example:

A javelin throws with an initial speed v0= 25m / sforming an angle of 45 ° to the horizontal. (a) What is the maximum range (b) and the maximum height reached? To calculate this movement one must divide the movement in vertical and horizontal.

To decompose the vector some components of trigonometry are required in its components: Generically we can call the angle formed by .

So: soon: and: soon: (a) in the horizontal direction (replacing the s of the function of space by x): being we have:

(1) Vertically (replacing H per y): being we have:

(2) And time is the same for both equations, so we can isolate it in (1), and substitute in (2):

(1) and , then: where substituting in (2):

(2)   and where the range is maximum . Then we have: but , then: solving this equation by Baskara formula: but So:  but So Replacing the problem data in the equation: (b) We know that when the height is maximum . So, starting from the Torricelli equation in vertical motion: and substituting the problem data in the equation, we get: 