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zaphod

  • 3 years ago

A particle is projected with speed v at an angle alpha to the horizontal. Find the speed of the particle when it is at height h

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  1. zaphod
    • 3 years ago
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    @UnkleRhaukus @ash2326

  2. ash2326
    • 3 years ago
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    @zaphod Particle's velocity has two components : 1) Horizontal Velocity= \(v\cos \alpha\) {remains unchanged throughout the length of the motion obviously we are ignoring the air friction } 2) Vertical Velocity=\(v \sin \alpha\) initially { decelerated by gravity} |dw:1349870216959:dw| Do you understand this part?

  3. zaphod
    • 3 years ago
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    yes now how do i get the height into this can u show the working

  4. ash2326
    • 3 years ago
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    Only \( v \sin \alpha\) is used for vertical motion. Using \[v^2-u^2=2as\] Taking upward direction to be positive We need to find vertical velocity when the particle reaches a height h \[v^2-u^2=2as\] s= h a=-g \[u=v\sin \alpha \] \[v^2-(u\sin \alpha)^2=2\times (-g)\times h\] now find v from this This will be the vertical velocity at height h |dw:1349870813000:dw|

  5. zaphod
    • 3 years ago
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    speed will be the resultant of v cos alpha and wt u found out?

  6. ash2326
    • 3 years ago
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    Note that this v is different from the v given in the question. Let it be x \[x|dw:1349871003737:dw|^2-(u\sin \alpha)^2=2\times (-g)\times h\]

  7. ash2326
    • 3 years ago
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    Yeah speed will be \[\sqrt {( v\ \cos \alpha)^2+x^2}\]

  8. ash2326
    • 3 years ago
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    \[x^2-(u\sin \alpha)^2=2\times (-g)\times h\]

  9. zaphod
    • 3 years ago
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    |dw:1349871122014:dw|

  10. ash2326
    • 3 years ago
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    Actually the velocity has two components v cos alpha and x Speed will be the magnitude

  11. ash2326
    • 3 years ago
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    yes

  12. zaphod
    • 3 years ago
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    thanks :)

  13. ash2326
    • 3 years ago
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    welcome (:

  14. Algebraic!
    • 3 years ago
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    \[speed = \sqrt{(V \sin \alpha)^{2}-2gh +(V \cos \alpha)^2}\] \[= \sqrt{(V^2 (\sin ^2 \alpha +\cos^2 \alpha)-2gh}\] \[= \sqrt{V^2 -2gh}\]

  15. zaphod
    • 3 years ago
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    thanks algebraic :)

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