Projectile Motion and the Range Formula

In summary, the conversation suggests using the identity sin(2x)=2sinxcosx to simplify the range formula for projectile motion, which results in the formula R= v^2 sin(2x)/g.
  • #1
tharindu
4
0
Hey Guys

Im wondering if anyone could help me simplify the range formula for projectile motion. So far I've got R=2v^2 sin(theta) cos(theta)/g.

Help will be appreciated. Thanks
 
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  • #2
Have you seen the identity sin(2x)=2sinxcosx?
 
  • #3
No i havent
 
  • #4
Using that identity, you can simplify the range formula easily.

Note that the identity can be derived from sin(a+b)=sin(a)cos(b)+sin(b)cos(a). Set a=b and you get sin(2a)=sin(a)cos(a)+sin(a)cos(a)=2sin(a)cos(a)
 
  • #5
so then the formula simplifies down to
R= v^2 sin(2x)/g ?
 

1. What is projectile motion?

Projectile motion is the motion of an object through the air or in a vacuum under the influence of gravity. It is a combination of horizontal (constant velocity) and vertical (constant acceleration) motion.

2. What is the range formula for projectile motion?

The range formula for projectile motion is R = (v2sin2θ)/g, where R is the range, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

3. How is the range formula derived?

The range formula is derived by considering the horizontal and vertical components of motion separately and using equations of motion to relate them. By setting the displacement in the horizontal direction equal to the displacement in the vertical direction, we can solve for the range formula.

4. What factors affect the range of a projectile?

The range of a projectile is affected by the initial velocity, the angle of launch, and the acceleration due to gravity. Air resistance and wind can also have an impact on the range.

5. Can the range of a projectile ever be infinite?

No, the range of a projectile is limited by the acceleration due to gravity and the initial velocity. Even if the angle of launch is 90 degrees, the object will eventually fall back down due to the force of gravity.

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