precalculus

Berry is standing at the edge of a hill that slopes downward and to the right. He notices that for every 5 feet you go in a horizontal direction, the hill drops by 2 feet. Berry places a ball at the edge of the hill (the origin of the coordinate system), and kicks the ball at a speed of 20 m/s and at an angle of 30o to the horizontal. The equation describing the ball’s height as a function of the horizontal distance it travels is given by . How far down the hill does the ball land?

asked by Anonymous
  1. the velocity has horizontal and vertical components
    Vx = 20(√3/2) = 17.32
    Vy = 20(1/2) = 10.00

    The horizontal and vertical positions of the ball are thus

    sx = 17.32t
    sy = 10.00t - 4.9t^2
    So, the x-y function of the height is
    y = 10.00(x/17.32) - 4.9(x/17.32)^2
    = -0.01633x^2 + 0.5774x

    The ground is descending with slope = -2/5 so the surface is given by

    y = -2/5 x

    So, where does the parabola intersect the line?

    -0.01633x^2 + 0.5774x = -0.4x
    x = 59.85
    y = -23.94

    so the distance down the slope is

    d = √(59.85^2 + 23.94^2) = 64.46 m

    posted by Steve

Respond to this Question

First Name

Your Answer

Similar Questions

  1. precalculus

    Berry is standing at the edge of a hill that slopes downward and to the right. He notices that for every 5 feet you go in a horizontal direction, the hill drops by 2 feet. Berry places a ball at the edge of the hill (the origin of
  2. math

    Mariano is standing at the top of a hill when he kicks a soccer ball into the air. The height of the hill is h feet, and the ball is kicked with an initial velocity of v feet per second. The height of the ball above the bottom of
  3. Math again sorry

    A roller coaster starts from a deck at an elevation of 20 feet above the ground. On the first hill it climbs 78 feet and then drops 85 feet. On the second hill the coaster climbs 103 feet and then drops 110 feet. How far below or
  4. Math help please

    Which hill described in the table is the steepest? Explain. Street|Horizontal distance|vertical rise Dixie |80 |40 hill | Bell |80 |20 hill | | Liberty|80 |60 hill | | A)Bell Hill;it rises 1 foot for every 4 feet of horizontal
  5. Math

    9.)Which hill described in the table is the steepest? Explain.' (Table) Street Horizontal Distance (ft) Vertical Rise Dixie Hill 60 20 Bell Hill 60 40 Liberty Hill 60 30 A.)Bel Hill; it rises 2/3 ft for every 1 food of horizontal
  6. math

    Street | Horizontal | Vertical rise Distance ft. |of street ft. _______|_____________|_______________ Dixie hill| 80. | 40 Bell hill | 80. | 20 Liberty hill| 80. | 60 Which hill is the steepest? Explain. A. Bell hill; it rises one
  7. Math "Need Help Asap"!

    9.)Which hill described in the table is the steepest? Explain.' (Table) Street Horizontal Distance (ft) Vertical Rise Dixie Hill 80 40 Bell Hill 80 20 Liberty Hill 80 60 A.Bell Hill; it rises 1 foot for every 4 feet of horizontal
  8. Math

    9.)Which hill described in the table is the steepest? Explain.' (Table) Street Horizontal Distance (ft) Vertical Rise Dixie Hill 80 40 Bell Hill 80 20 Liberty Hill 80 60 A.)Bell Hill; it rises 1 foot for every 4 feet of horizontal
  9. Math

    Which hill described in the table is the steepest? (Table) Street: Horizontal (ft): Vertical Rise (ft): Dixie Hill 60 20 Bell Hill 60 40 Liberty Hill 60 30 A. Bell Hill; it rises 2/3 foot for every 1 foot of horizontal travel. B.
  10. math

    Which hill described in the table is the steepest? (Table) Street: Horizontal (ft): Vertical Rise (ft): Dixie Hill 60 20 Bell Hill 60 40 Liberty Hill 60 30 A. Bell Hill; it rises 2/3 foot for every 1 foot of horizontal travel. B.

More Similar Questions