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Summersnow8

  • one year ago

John stands on the edge of a deck that is 40.0 m above the ground and throws a rock straight up that reaches a height of 15.0 m above the deck. What is the initial speed of the rock in m/s? which i solved correctly and it is 17.1 Assuming the rock in the previous question misses the deck on the way down, how fast (in m/s) will the rock be moving when it hits the ground? @ybarrap @lightgrav

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  1. Summersnow8
    • one year ago
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    i used the equation \[2as = V _{f}^{2} - V{i}^{2}\]

  2. anonymous
    • one year ago
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    so, use that correct answer in the same statement (equation) as before, but solve it for v_f ... remember that (now) a is in the same direction as s (both downward) so 2as is positive.

  3. anonymous
    • one year ago
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    (or, you could start with v_i = 0, but watch the rock fall 55m

  4. Summersnow8
    • one year ago
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    so, \[2 (-9.8)(-40) = Vf ^{2} - (17.1)^{2}\]

  5. anonymous
    • one year ago
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    looks right so far

  6. Summersnow8
    • one year ago
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    so vf would be 32.8?

  7. anonymous
    • one year ago
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    yes, 55m is almost 4x the upward 15m (so v should be almost double)

  8. ybarrap
    • one year ago
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    You got it! Another way to look at this - $$ V_f^2 = V_i^2 + 2gs $$ Where \(V_i=0\), the speed of the rock at the highest point. \(s\) is is the distance the rock is above the deck plus the height the deck is above the ground: 15+40=55. Now you have everything to solve. You've got the right approach either way!

  9. Summersnow8
    • one year ago
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    so is 32.8 the answer? i was told to use the equation i listed

  10. anonymous
    • one year ago
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    His eq'n is the same as yours, just re-arranged for v_f

  11. ybarrap
    • one year ago
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    Yep! $$ V_f^2 = V_i^2 + 2gs=0-2\times9.81\times55\\ \implies V_f=32.8~m/s $$

  12. ybarrap
    • one year ago
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    *Negative, because rock is going down: $$ V_f^2 = V_i^2 + 2gs=0-2\times9.81\times55\\ \implies V_f=\color{red}{-}32.8~m/s $$

  13. Summersnow8
    • one year ago
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    ..... negative?

  14. ybarrap
    • one year ago
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    Just indicates direction, downward. Up is positive

  15. anonymous
    • one year ago
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    the same direction as the acceleration.

  16. Summersnow8
    • one year ago
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    it says it's wrong

  17. anonymous
    • one year ago
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    ooh, they asked for _speed_ (how fast) not velocity :-(

  18. ybarrap
    • one year ago
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    speed is magnitude, velocity includes directional information. So speed would just be 32.8 m/s

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