Question

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.

Answer 1

x is the horizontal position

Answer 2

determine y for zeros; that should give you time in the air, use that t to determine the x

Answer 3

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?

Answer 4

i got no keyboard talents on this little laptop

Answer 5

type up y with the info for me and ill let you know if its good

Answer 6

find t from y first, not from x

Answer 7

the only reason for the fence info is either for clutter, or to test if the ball actually makes it over the fence

Answer 8

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

Answer 9

x=105cos(40)(.235) = 18.9 units of measure

Answer 10

i see my error, a = -16, not 2.5

Answer 11

shouldn't a= 16/105cos40?

Answer 12

t = (-105sin(40) + sqrt(105^2sin^2(40)-4(-16)(2.5))) /(2(-16))

t = 4.255 is better :)

Answer 13

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

Answer 14

i still think a=16/105cos40

Answer 15

why?

Answer 16

t = 4.255 when i fix my errors

Answer 17

because t= x/105cos40 so when 16 times x. it would come out to be (16x/105cos40)^2

Answer 18

you could prolly try that route, but its quite alot of extra work

Answer 19

at any rate we got 2 scenarios to test out