Range Formula Projectile Motion Physics

Following are the formula of projectile motion which is also known as trajectory formula. This video explains how to use the equation why a launch angle of 45 gives the maximum range and why complementary angles give the same range.

Projectile Motion Formula Formula For Projectile Motion Projectile Motion Physics Mechanics Physics

The time of flight of a projectile motion is the time from when the object is projected to the time it reaches the surface.

Range formula projectile motion physics. Projection angle θ 0. Where v x is the velocity along the x axis v xo is initial velocity along the x axis v y is the velocity along the y axis. Vy v sin α time of flight.

As we discussed previously t t depends on the initial velocity magnitude and the angle of the projectile. From that equation we ll find t which is the time of flight to the ground. T 2 vy g range of the projectile.

Derivation of the horizontal range formula. The projectile range is the distance traveled by the object when it returns to the ground so y 0. The horizontal range of a projectile is defined as the horizontal displacement of a projectile when the displacement of the projectile in the y direction is zero.

The following applies for ranges which are small compared to the size of the earth. For longer ranges see sub orbital spaceflight the maximum horizontal distance traveled by the projectile neglecting air resistance can. Horizontal range x u cos θ t.

Vx v cos α vertical velocity component. Therefore we derive it using the kinematics equations. Vertical velocity after t seconds v y u sin θ gt.

T 2 uy g t 2 u sinθ g t 2 u y g t 2 u sin. T 2 v sin α g. In physics assuming a flat earth with a uniform gravity field and no air resistance a projectile launched with specific initial conditions will have a predictable range.

To find the formula for the range of the projectile let s start from the equation of motion. 0 v t sin α g t 2. Mathrm r dfrac u 2 sin 2 θ g range of trajectory.

Most of the basic physics textbooks talk on the topic of horizontal range of the projectile motion. Velocity of projectile after t seconds projectile motion on inclined plane formulas. R 2 vx vy g.

Using this we can rearrange the parabolic motion equation to find the range of the motion. Launching the object from the ground initial height h 0. Uff that was a lot of calculations.

Acceleration of gravity g 0. The range of the motion is fixed by the condition mathrm y 0. Let s sum that up to form the most essential projectile motion equations.

The range of a trajectory is shown in this figure. A x 0 v x v 0x triangle x v 0x t a y g v y v 0y gt. When any object is thrown with velocity u making an angle α from horizontal at a plane inclined at an angle β from horizontal then.

The projectile is the object while the path taken by the projectile is known as a trajectory.

Formula Of Projectile Motion Physics Formulas Physics Projectile Motion