Deriving Projectile Motion Equations

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To derive the equations for the range and total time-of-flight of a projectile launched with initial speed v from height h at angle Q, start by determining the horizontal and vertical components of the initial velocity: Vox = vcosQ and Voy = vsinQ. The range can be calculated using the formula range = vt - 0.5gt^2, where t is the total time of flight. The time of flight is derived from the vertical motion equation: time = (vsinQ + sqrt((vsinQ)^2 + 2gh)) / g. By substituting specific values for initial speed, angle, and height, the equations can be applied to solve for the projectile's motion. Understanding these components is crucial for accurately calculating projectile trajectories.
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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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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.
 

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