Solving Projectile Motion: Calculating Initial Velocity with Known Variables

In summary, to calculate the initial velocity of an object needed to travel a certain distance from atop a given height, one can use the equations provided in the link given. These equations take into account variables such as height, angle, distance traveled, acceleration of gravity, and mass of the object. By simplifying and solving for the initial velocity, one can determine the velocity needed for the object to reach its desired distance. However, it is important to note that this method may not work if the launch point is not at the same level as the landing and if the time is unknown.
  • #1
Sundaze
3
0
How can one go about calculating the initial velocity of an object needed to travel a certain distance, starting from atop a given height.

Variables known: height, angle, distance traveled, acceleration of gravity, mass of object
Not known: initial and final velocity, time
 
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  • #2
Sundaze said:
How can one go about calculating the initial velocity of an object needed to travel a certain distance, starting from atop a given height.

Variables known: height, angle, distance traveled, acceleration of gravity, mass of object
Not known: initial and final velocity, time
Use the http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra4".

AM
 
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  • #3
These do not work since the launch point is not at the same level as the landing. And time is unknoen.
 
  • #4
Sundaze said:
These do not work since the launch point is not at the same level as the landing. And time is unknoen.

The range x = v*cosθ*t.

So t = x/v*cosθ

-y = v*sinθ*t - 0.5*g*t^2

-y = v*sinθ*x/v*cosθ - 0.5*g*(x/v*cosθ)^2

-y = x*tanθ - 0.5*g*x^2/v^2*cos^2(θ)

Now simplify and solve for v.
 
  • #5
Sundaze said:
These do not work since the launch point is not at the same level as the landing. And time is unknoen.
If you scroll down on the link I gave you, you will see how to analyse the problem.

AM
 
  • #6
rl.bhat said:
The range x = v*cosθ*t.

So t = x/v*cosθ

-y = v*sinθ*t - 0.5*g*t^2

-y = v*sinθ*x/v*cosθ - 0.5*g*(x/v*cosθ)^2

-y = x*tanθ - 0.5*g*x^2/v^2*cos^2(θ)

Now simplify and solve for v.

Thanks, it all makes sense now.
 

1. What is projectile motion?

Projectile motion is the motion of an object that is launched or thrown into the air and moves along a curved path under the influence of gravity.

2. What factors affect projectile motion?

The factors that affect projectile motion include the initial velocity, angle of launch, air resistance, and the force of gravity.

3. How is the trajectory of a projectile calculated?

The trajectory of a projectile can be calculated using the equations of motion, which take into account the initial velocity, angle of launch, and acceleration due to gravity.

4. What is the difference between horizontal and vertical motion in projectile motion?

In projectile motion, horizontal motion is constant and unaffected by gravity, while vertical motion is affected by gravity and follows a parabolic path.

5. How can projectile motion be applied in real life?

Projectile motion has many applications in real life, including sports such as basketball, baseball, and golf, as well as in engineering and military operations, such as launching projectiles from cannons or missiles.

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