Physics

# How those air resistance affect the vertical and horizontal velocity of a projectile calculation?

345 ###### 2011-11-22 18:44:13

Air resistance acts against the motion of the object. Whatever range you get when assuming no air resistance is too large.

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## Related Questions If you can ignore the effects of air resistance, the horizontal component of projectile velocity doesn't change at all.   That's true if you ignore air resistance, as we customarily do in order to simplify discussions of projectile motion. It's true because there's no horizontal force acting on the projectile, to increase or decrease the horizontal component of its velocity. No, the projectile accelerates in the vertical direction, due to gravity, but not at all in the horizontal direction. The projectile's horizontal velocity will remain constant as long as air resistance is negligible. The horizontal velocity of the projectile (and the air resistance if known) will determine the horizontal distance traveled and the time required. In projectile motion, the force of gravity has no influence on the horizontal component of velocity. If there wouldn't be air resistance and gravity is the only thing that is effecting the projectile, the projectile will start to fall but it horizontal velocity will remain the same. So it would slow down, it would only change height. Because there's no horizontal force acting on it that would change its horizontal component of velocity. (In practice, that's not completely true, since the frictional 'force' of air resistance acts in any direction. But outside of air resistance, there's nothing else acting horizontally on the projectile.) Since the velocity is constant due to the fact that there are no external forces acting in the horizontal direction, if you neglect air resistance, therefore, the horizontal velocity of a projectile is constant.  A projectile that is thrown with an initial velocity,that has a horizontal component of 4 m/s, its horizontal speed after 3s will still be 4m/s. The a projectile that goes vertically up reaches its maximum height, its speed will be zero. In the more general case, the vertical component of its velocity will be zero; however, the projectile may also have a horizontal component. In summary, assuming that air resistance is negligible: * The horizontal component of velocity doesn't change over time. At the highest point, it will be the same to the original horizontal component of velocity. * The vertical component of velocity will be zero at the highest point. Because there is vertical force acting on the projectile (hint: the force of gravity), whereas there is no horizontal force acting on it. A projectile is a free-falling object that also has some horizontal velocity. That combination is called "projectile motion". In the absence of air resistance, its shape is always a parabola. In the usual simple treatment of projectile motion, the horizontal component of the projectile's velocity is assumed to be constant, and is equal to the magnitude of the initial (launch) velocity multiplied by the cosine of the elevation angle at the time of launch. One that goes directly up - the velocity having no horizontal component. The horizontal component of velocity for a projectile is not affected by the vertical component at all. Horizontal component is measured as xcos(theta) Vertical component is measured as xsin(theta) Whereas theta is the angle, and x is the magnitude, or initial speed. In projectile motion, since , there's no force in the horizontal direction which can change the horizontal motion therefore the horizotal velocity remains conserved Vx=Vox= Vocos theta by using above formula , constant horizontal initial or final velocity can be found. since Initial = final horizontal velocity. -- horizontal component of velocity -- horizontal component of acceleration (zero) -- vertical component of acceleration (g) the horizontal component remain unchanged because there in no acceleration in horizontal direction The range of a projectile on level ground, when air resistance is ignored, isd = v2*sin(2x)/g wherev is the intial velocity of the projectile,x is the angle above the horizontal at which the projectile is launchedandg is the acceleration due to the earth's gravity.This function is a maximum when x = 45 degrees and so d is smaller for other values of x.The range of a projectile on level ground, when air resistance is ignored, isd = v2*sin(2x)/g wherev is the intial velocity of the projectile,x is the angle above the horizontal at which the projectile is launchedandg is the acceleration due to the earth's gravity.This function is a maximum when x = 45 degrees and so d is smaller for other values of x.The range of a projectile on level ground, when air resistance is ignored, isd = v2*sin(2x)/g wherev is the intial velocity of the projectile,x is the angle above the horizontal at which the projectile is launchedandg is the acceleration due to the earth's gravity.This function is a maximum when x = 45 degrees and so d is smaller for other values of x.The range of a projectile on level ground, when air resistance is ignored, isd = v2*sin(2x)/g wherev is the intial velocity of the projectile,x is the angle above the horizontal at which the projectile is launchedandg is the acceleration due to the earth's gravity.This function is a maximum when x = 45 degrees and so d is smaller for other values of x. A projectile will travel on a straight line unless external forces act upon it. Gravity will pull the projectile downward, i.e. affect its vertical velocity component. This is why the projectile will decelerate upwards, reach a maximum elevation, and accelerate back down to earth. The force vector of air resistance points in the opposite direction of motion, slowing the projectile down. For example, If the projectile is going forward and up, air resistance is pushing it backwards (horizontal component) and down (vertical component). Without air resistance, there is no external force acting upon the horizontal velocity component and the projectiles ground speed will stay constant as it gains altitude and falls back down to earth. If space were entirely empty this would be true, but even minute gravitational forces can change the trajectory and velocity of a projectile.

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