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 .

Comments:

- 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 *v _{0}= 25m / s*forming 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:*