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anonymous

  • one year ago

Been stuck for hours The function H(t) = −16t2 + 90t + 50 shows the height H(t), in feet, of a projectile after t seconds. A second object moves in the air along a path represented by g(t) = 28 + 48.8t, where g(t) is the height, in feet, of the object from the ground at time t seconds. Part A: Create a table using integers 1 through 4 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points) Part B: Explain what the solution from Part A means in the context of the problem. (4 points)

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  1. anonymous
    • one year ago
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    @mathstudent55

  2. anonymous
    • one year ago
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    Anybody got an idea? I'm basically just needing help on part A.

  3. mathstudent55
    • one year ago
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    Start by evaluating both functions at t = 1, t = 2, t = 3, t = 4

  4. anonymous
    • one year ago
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    16 90 28 48?

  5. anonymous
    • one year ago
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    @mathstudent55

  6. mathstudent55
    • one year ago
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    How did you get 16?

  7. mathstudent55
    • one year ago
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    H(t) = −16t2 + 90t + 50 Let t = 1. What do you get for H(1) ?

  8. anonymous
    • one year ago
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    I just found it, idk how i got it, I guessed on it

  9. anonymous
    • one year ago
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    How do i find h(1)

  10. anonymous
    • one year ago
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    Like, i'm 100% lost on how I make these, I found some functions but idk how to graph them, can you explain?

  11. mathstudent55
    • one year ago
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    H(t) = −16t2 + 90t + 50 To find H(1) you replace t with 1, and you evaluate the expression. H(1) = -16(1)^2 + 90(1) + 50

  12. mathstudent55
    • one year ago
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    H(1) = -16 + 90 + 50 = 124 Now you need H(2). Replace t with 2 in the H(t) function and evaluate the right side. H(2) = -16(2^2) + 90(2) + 50

  13. anonymous
    • one year ago
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    How do I evaluate it? Like how'd you get that

  14. anonymous
    • one year ago
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    1 is H(1) = -16 + 90 + 50 = 124, I need to solve for 2,3, and 4?

  15. anonymous
    • one year ago
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    @mathstudent55

  16. anonymous
    • one year ago
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    I need to find 2,3,4 but how?

  17. mathstudent55
    • one year ago
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    Evaluating an expression is just using arithmetic to calculate what it is equal to.

  18. mathstudent55
    • one year ago
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    For t = 2, you get H(2) = -16(2^2) + 90(2) + 50 What is the right side equal to?

  19. anonymous
    • one year ago
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    H(2) = -16(2v2) + 180 + 50?

  20. mathstudent55
    • one year ago
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    If I asked you what is 2 + 2, would you answer 2 + 2, or would you answer 4?

  21. anonymous
    • one year ago
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    H(2) -16^4 + 230?

  22. mathstudent55
    • one year ago
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    good, keep going

  23. anonymous
    • one year ago
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    H(2) - 64 + 230?

  24. mathstudent55
    • one year ago
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    good

  25. mathstudent55
    • one year ago
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    H(2) = - 64 + 230?

  26. anonymous
    • one year ago
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    So it'd be H(2) = 294, or since 64 is negative would it be H(2) = 166?

  27. mathstudent55
    • one year ago
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    H(2) = 166

  28. mathstudent55
    • one year ago
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    So far we have: H(1) = 124 H(2) = 166 Now we still need H(3) and H(4) for function H(t) H(t) = −16t2 + 90t + 50 H(3) = -16(3)^2 + 90(3) + 50

  29. anonymous
    • one year ago
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    H(3) = -96 + 320

  30. anonymous
    • one year ago
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    H(3) = 224?

  31. mathstudent55
    • one year ago
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    No. First do 3^2

  32. anonymous
    • one year ago
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    9

  33. mathstudent55
    • one year ago
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    H(3) = -16(3)^2 + 90(3) + 50 H(3) = -16(9) + 90(3) + 50 Now do -16 * 9. You already have 90(3) + 50 = 320

  34. anonymous
    • one year ago
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    -144

  35. anonymous
    • one year ago
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    -144 + 270 + 50 right?

  36. mathstudent55
    • one year ago
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    yes

  37. anonymous
    • one year ago
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    H(3)=176?

  38. mathstudent55
    • one year ago
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    Correct. Now we need H(4) H(4) = -16(4)^2 + 90(4) + 50 Remember to start with 4^2 then multiply that by -16

  39. anonymous
    • one year ago
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    156?

  40. mathstudent55
    • one year ago
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    I got 154 H(4) = -16(4)^2 + 90(4) + 50 = -256 + 360 + 50 =

  41. mathstudent55
    • one year ago
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    Ok. We have now function H(t) evaluated at t = 1, t = 2, t = 3, t = 4. Now we need to do the same for function g(t)

  42. anonymous
    • one year ago
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    Four more for g(t)?

  43. anonymous
    • one year ago
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    Alright, what's the functions?

  44. anonymous
    • one year ago
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    You there math?

  45. mathstudent55
    • one year ago
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    The g(t) function is simpler. Just multiply the number (1, 2, 3, 4) by 48.8, then add to 28. g(t) = 28 + 48.8t g(1) = 28 + 48.8(1) = g(1) = 28 + 48.8(2) = g(1) = 28 + 48.8(3) = g(1) = 28 + 48.8(4) =

  46. anonymous
    • one year ago
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    g(1) =76.8 g(2)=125.6 g(3)= 174.4 g(4)= 223.2

  47. mathstudent55
    • one year ago
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    Correct. Great job on function g(t). Now we place all values in a table like part A asks for. |dw:1437421534524:dw|

  48. anonymous
    • one year ago
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    Great, now that the graph's done what now? It says something about what 2 seconds match, or something

  49. mathstudent55
    • one year ago
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    Part A asks to look at the table and see between which two times the functions H and g have the same value.

  50. mathstudent55
    • one year ago
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    |dw:1437421963065:dw|

  51. mathstudent55
    • one year ago
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    Notice that at t = 3, H = 176 and g = 174.4, H is higher, but at t = 4, H = 154, and g = 223.2, g is higher. That means at some time between 3 and 4, the functions must have the same value.

  52. anonymous
    • one year ago
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    I noticed, so that's the answer it requires?

  53. mathstudent55
    • one year ago
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    The answer to part A is that the objects are at the same height sometime between 3 and 4 seconds.

  54. mathstudent55
    • one year ago
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    Then the answer to part B is that the objects hit each other at that time between 3 and 4 seconds when their paths cross in the air.

  55. anonymous
    • one year ago
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    Thank you so much, I honestly would've never figured out how to work this problem. Thanks for the help :))

  56. mathstudent55
    • one year ago
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    You are welcome.

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