Deriving Projectile Motion Equations

In summary, the conversation discussed deriving algebraic expressions for the range and total time-of-flight of a projectile launched at an angle and from a given height. The equations for range and time-of-flight were provided, but there was uncertainty about how to derive them. The suggested approach was to consider the ball's motion after being launched and use equations for horizontal and vertical components of speed and motion. The example of a projectile launched with initial speed 100 m/s, angle 30 degrees, and height 2 m was discussed as a potential application of these equations.
  • #1
charris316
2
0

Homework Statement


Derive algebraic expressions for the range and total time-of-flight of a projectile launched with initial speed v, from a height h, and at an angle Q, above the horizontal. We were given the final equations but I am unsure of how to derive them.


Homework Equations


range=vt-.5gt^2, where g is the acceleration due to gravity and t is the time in seconds.

time= (vsinQ+((vsinQ)^2+2gh)^.5)/g


The Attempt at a Solution


Considering the ball, after it has been launched:
Fx=0
Vox=vcosQ
Fy=mg
Voy=vsinQ

?
 
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  • #2
If you were given initial speed 100, angle 30 degrees, height 2 m
could you solve it? If so, you can just replace the 100, 30 and 2 in every place with the given letters.

The first step is to find the horizontal and vertical components of the speed.
Then write equations for the vertical and horizontal motions.
 

1. What is a motion equation?

A motion equation is a mathematical expression that describes the motion of an object in terms of its position, velocity, and acceleration. It is used to predict the future position of an object based on its initial conditions and the forces acting upon it.

2. How is a motion equation derived?

A motion equation is derived using the principles of Newton's laws of motion and the fundamental equations of kinematics. It involves using calculus to determine the relationship between an object's position, velocity, and acceleration at any given time.

3. What are the variables in a motion equation?

The variables in a motion equation include time, position, velocity, and acceleration. Time is usually denoted as "t", position as "x", velocity as "v", and acceleration as "a". The values of these variables may change depending on the specific motion being described.

4. How accurate are motion equations?

Motion equations are highly accurate when the initial conditions and forces acting upon an object are known and can be predicted with a high degree of precision. However, they may become less accurate when dealing with complex systems or when there are external factors that cannot be accounted for.

5. Can motion equations be used for all types of motion?

Yes, motion equations can be used for all types of motion, including linear, circular, and projectile motion. However, the specific equations used may vary depending on the type of motion being described. For example, the equations for projectile motion would differ from those for linear motion.

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