Solving for the Projection Angle: Range and Maximum Height Relationship

In summary, if you are given the angle and velocity of a projectile, you can find its range and maximum height.
  • #1
chitownfireman
3
0
My teacher gave me this problem today and I have tried everything I know but I still haven't found the right answer. If anyone knows how to solve it, please share. Thanks

At what projection angle will the range of a projectile equal its maximum height?


Hint: 2 sin θ cos θ = sin 2 θ
 
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  • #2
Presumably you've either been given a formula for the range of a projectile, or know the kinematic equations and can derive such an equation. Do the usual thing, split up into vertical and horizontal components, and solve for each separately.

You need to show some work before you get any real help, and should note that solutions are not provided on these forums at all. In future, also, please post in the homework forums. Oh, and welcome to PF.
 
  • #3
Sorry about that mate, thanks for the advice.
 
  • #4
the angle is 76
 
  • #5
Thanks mate, but I never wanted the exact answer, I just wanted a push in the right direction. You may be right, but I am currently trying to figure it out, but thanks for the input.
 
  • #6
Let A be the angle and u be the velocity of projection and g ( accel due to gravity)
Range (R) = u^2sin A^2/2g

Max Height(H)=u^2sin2 A/g

sin 2 A = 2 sin A cos A

equate R and H ( since they should be equal)..

u will get sin A/cos A = 4

but sin A/cos A = tan A

therfore A should be 76 degrees...
 
  • #7
saiaspire said:
Let A be the angle and u be the velocity of projection and g ( accel due to gravity)
Range (R) = u^2sin A^2/2g

Max Height(H)=u^2sin2 A/g

sin 2 A = 2 sin A cos A

equate R and H ( since they should be equal)..

u will get sin A/cos A = 4

but sin A/cos A = tan A

therfore A should be 76 degrees...
you're not suppose to give out full solutions or the answer.
 

1. What is projection angle?

Projection angle is the angle at which an object or image is projected onto a surface. It is typically measured from the horizontal plane and can affect the size, shape, and distortion of the projected image.

2. How is projection angle calculated?

The projection angle can be calculated using trigonometric functions based on the distance from the projector to the surface and the height at which the projector is mounted. It can also be determined by the type of projection, such as 2D or 3D, and the specific projection method being used.

3. What is the ideal projection angle for optimal image quality?

The ideal projection angle varies depending on the type of projector and the intended use. In general, a perpendicular projection angle (90 degrees) will result in the most accurate and least distorted image. However, for certain projection techniques, such as rear projection, a specific angle may be recommended for optimal viewing.

4. How does projection angle affect image distortion?

The projection angle can greatly impact image distortion, particularly in 3D projections. A larger angle can result in more distortion, while a smaller angle can create a more accurate image. Additionally, the shape and angle of the surface being projected onto can also affect distortion.

5. Can the projection angle be adjusted?

Yes, the projection angle can be adjusted by changing the distance and/or height of the projector, or by using specialized lenses or software to alter the angle. Some projectors also have manual or automatic keystone correction capabilities to adjust the angle and reduce distortion in the projected image.

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