Where does this kinematics equation come from?

  • Thread starter mybrohshi5
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In summary, g(t)/vox=tan(theta) is a formula for calculating the angle below the horizontal that a projectile will be moving after time t, given the acceleration due to gravity (g), initial velocity in the x direction (vox), and time (t). It can be derived from the equations vsinθ = gt and vcosθ = vx0.
  • #1
mybrohshi5
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g(t)/vox=tan(theta)

g= acceleration due to gravity (9.8m/s^2)
t= time
vox = initial velocity in the x direction

Where does this equation come from?? someone told me to use this to help me solve one of my homework problems and it worked but i have never seen it before and am having a hard time to figure out where the components of the equation actually come from?

could anyone help explain this equation to me?

thank you
 
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  • #2
mybrohshi5 said:
g(t)/vox=tan(theta)

g= acceleration due to gravity (9.8m/s^2)
t= time
vox = initial velocity in the x direction
This looks like a formula for calculating the angle below the horizontal that a projectile will be moving after time t after being released with a purely horizontal speed of V0x. It's just tanθ = Vy/Vx. Vy = at = gt.
 
  • #3
Hi mybrohshi5! :smile:

(have a theta: θ and try using the X2 tag just above the Reply box :wink:)

If at time t, the angle is θ and the speed is v, then

vsinθ = gt

vcosθ = vx0,

so tanθ = gt/vx0 :wink:
 
  • #4
thank you both! that makes complete sense now.
 
  • #5


This kinematics equation is known as the "vertical motion equation" and it is derived from the basic principles of kinematics and Newton's laws of motion. The equation relates the acceleration due to gravity, initial velocity in the x direction, and time to the angle of the trajectory, represented by theta. It is commonly used to solve problems involving objects in free fall or projectile motion. The equation can be derived using basic mathematical principles and physical laws, and has been extensively tested and verified through experiments. It is a fundamental equation in the study of motion and is widely used in various fields of science and engineering. I would recommend reviewing the principles of kinematics and Newton's laws of motion to gain a better understanding of this equation and its application.
 

1. Where does the kinematics equation for displacement come from?

The kinematics equation for displacement, s = ut + 1/2at^2, comes from the basic principles of motion and calculus. It is derived from the definition of acceleration, which is the rate of change of velocity over time. By integrating this definition, we can derive the equation for displacement.

2. How is the kinematics equation for velocity derived?

The kinematics equation for velocity, v = u + at, is derived by taking the derivative of the equation for displacement. This means we are finding the rate of change of displacement over time, which is velocity. By taking the derivative, we can find the instantaneous velocity at any given time.

3. What is the origin of the kinematics equation for acceleration?

The kinematics equation for acceleration, a = (v-u)/t, comes from the definition of acceleration, which is the rate of change of velocity over time. By rearranging this definition, we can solve for acceleration and get the equation in its commonly used form.

4. Why do we use kinematics equations in physics?

Kinematics equations are used in physics to describe the motion of objects. They allow us to calculate the position, velocity, and acceleration of an object at any given time, given some initial conditions. These equations are also useful for predicting the future motion of an object based on its current state.

5. Can the kinematics equations be applied to all types of motion?

Yes, the kinematics equations can be applied to all types of motion, as long as the motion is along a straight line and the acceleration is constant. This is known as linear motion. For more complex types of motion, such as circular or projectile motion, we use other equations that take into account the changing direction of motion.

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