anonymous
  • anonymous
Parametric Equations. Use the following parametric equation: x=(vo cos theta)t y=h+(vo sin theta)t-16t^2 h=ft above ground vo= ft/second theta= angle from the horizontal. The right field fence in a ballpark is 10 ft high and 314 ft from home plate. A baseball is hit at a point 2.5 ft above the ground. It leaves the bat at an angle of theta=40 degree, with the horizontal at the speed of 105 ft per second. Q: Find the horizontal distance that the baseball travels.
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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amistre64
  • amistre64
x is the horizontal position
amistre64
  • amistre64
determine y for zeros; that should give you time in the air, use that t to determine the x
anonymous
  • anonymous
Yes.. but then you must plug in all the given information, and then find "t" from the x equation . then plug in "t" into the y equation i did all that but my number still comes out wrong T.T Can someone possibly plug in the numbers and help me realize my wrong?

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amistre64
  • amistre64
i got no keyboard talents on this little laptop
amistre64
  • amistre64
type up y with the info for me and ill let you know if its good
amistre64
  • amistre64
find t from y first, not from x
amistre64
  • amistre64
the only reason for the fence info is either for clutter, or to test if the ball actually makes it over the fence
anonymous
  • anonymous
1 Attachment
amistre64
  • amistre64
2.5+105sin40 t -16 t^2 = 0 t = (-105sin(40) + sqrt(105^2sin^2(40)-4(-16)(2.5))) /2(2.5) http://www.wolframalpha.com/input/?i=t+%3D+%28-105sin%2840%29+%2B+sqrt%28105%5E2sin%5E2%2840%29-4%28-16%29%282.5%29%29%29+%2F%282%282.5%29%29 t = .235 seconds if i entered those right
amistre64
  • amistre64
x=105cos(40)(.235) = 18.9 units of measure
amistre64
  • amistre64
i see my error, a = -16, not 2.5
anonymous
  • anonymous
shouldn't a= 16/105cos40?
amistre64
  • amistre64
t = (-105sin(40) + sqrt(105^2sin^2(40)-4(-16)(2.5))) /(2(-16)) t = 4.255 is better :)
amistre64
  • amistre64
now when x = the distance of the fence we gain a t value to test in y to see if we even clear the fence to begin with
anonymous
  • anonymous
i still think a=16/105cos40
amistre64
  • amistre64
why?
amistre64
  • amistre64
t = 4.255 when i fix my errors
anonymous
  • anonymous
because t= x/105cos40 so when 16 times x. it would come out to be (16x/105cos40)^2
amistre64
  • amistre64
you could prolly try that route, but its quite alot of extra work
amistre64
  • amistre64
|dw:1332389066506:dw|at any rate we got 2 scenarios to test out
anonymous
  • anonymous
I’m so confused T.T
amistre64
  • amistre64
x=314=105cos(40) t t = 314/(105cos(40)); if y is greater than 10 when t = this value, we clear the fence
amistre64
  • amistre64
parametrics just measure things independant of each other.
anonymous
  • anonymous
where did you get 314. T.T
amistre64
  • amistre64
y = 2.5 + 105sin(40)(314)/(105cos(40))-16(314/(105cos(40)))^2 http://www.wolframalpha.com/input/?i=y+%3D+2.5+%2B+105sin%2840%29%28314%29%2F%28105cos%2840%29%29-16%28314%2F%28105cos%2840%29%29%29%5E2 it clears the fence by over 10 feet :)
amistre64
  • amistre64
314 is the distance the fence is from homeplate
anonymous
  • anonymous
oh yes.
amistre64
  • amistre64
so if we clear the fence, and we do, we can go with our original finding of t=4.255 into x to determine the distance traveled
anonymous
  • anonymous
yes.

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