Projectiles - person kicks a soccer ball at an angle

Projectiles -- person kicks a soccer ball at an angle

Homework Statement

a) A person kicks a soccer ball at an angle and sends it in the air. What angle of projection between 0 and 90 degrees produces the greatest initial vertical component? Greatest intital horizontal component?

Homework Equations

Using cosine, sine of triangle.

The Attempt at a Solution

Would it be 90 degrees for the intital vertical component and 0 degrees for the horizontal component? Is that possible?

If the intial angle is 90 or 0 then it would be linear motion in vertical or horizontal direction respectively, so if you need maximum vertical and horizontal component for given intial velocity in a projectile then it must be 45 degree.

If the intial angle is 90 or 0 then it would be linear motion in vertical or horizontal direction respectively, so if you need maximum vertical and horizontal component for given intial velocity in a projectile then it must be 45 degree.

So the angle for both initial horizontal and vertical component is 45 degrees?

haruspex
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if you need maximum vertical and horizontal component
Not sure that means anything. If you maximise the one you will not maximise the other. It certainly isn't what the question asks for. Coco12's answer looks right to me.

Let u, ux, uy be the intial velocity, x component of velocity, y component of velocity respectively.

We know ux=u*cosθ , uy=u*sinθ where o<=θ<=90.

So θ=45 is the only angle for which both components are maximum. You can verify it by plotting sine and co sine curve graphically and see it.

Last edited:
haruspex
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Let u, ux, uy be the intial velocity, x component of velocity, y component of velocity.

We know ux=u cosθ , us=u*sinθ where o<=θ<=90.

So θ=45 is the only angle for which both components are maximum.
Neither is maximised at 45 degrees. 45 degrees maximises max{ux, uy}, but that is not the question.

He wants to find the maximum vertical and horizontal component of the displacement vector?

He wants to find the maximum vertical and horizontal component of the displacement vector?

I know that 45 degrees gives you a max range value however the question is asking for the greatest intital vertical component and the greatest intital horizontal component, so wouldn't that be different or?

Intial vertical and horizontal component of what? Wether it is displacement, velocity, acceleration.check the question carefully!

haruspex
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Intial vertical and horizontal component of what? Wether it is displacement, velocity, acceleration.check the question carefully!
Initial displacements are necessarily zero. It can only be referring to velocity components.

It doesn't indicate whether it is velocity or displacement, etc. it just says intital horizontal and vertical components

haruspex
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It doesn't indicate whether it is velocity or displacement, etc. it just says intital horizontal and vertical components
So what would the initial vertical displacement be? Is asking for its maximum a sensible question?

Either acceleration and displacement would make no sense. So it must be velocity in that case the answer is 45 degree.

nasu
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Yes, it must be velocity. But the answer is not 45 degree. For a given magnitude of velocity, at what angle is the vertical projection the largest?

90 degree. Whether the question is find the angle which maximizes both or just separately vertical and horizontal component. If it was the latter case then the for vertical and horizontal component the angles are 90 and 0 respectively.

nasu
Gold Member
The question is clear. It asks two questions. One about vertical component. The second about horizontal component. They are even in two different sentences.
And 45 degrees does not maximize any of the two component. Either one can be increased more by changing the angle from 45 degrees.

45 degrees maximizes the range but this is another story.