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A rocket is launched from the ground and follows a parabolic path represented by the equation y= -x squared + 10x. At the same time, a flare is launched from the height of 10 feet and follows a straight path represented by the equation y= -x + 10. Will these two object interest? If they do interest, where will it be?

Respuesta :

apologiabiology
x=horizontal position
y=vertical position (height)
y=-x²+10x
y=-x+10
intersect is when the position (x,y) on the path is the same on both

set equal to each other
-x²+10x=-x+10
times -1 both sides
x²-10x=x-10
add 10 to both sides and minus x both sides
x²-9x+10=0
factor
(x-10)(x+1)=0

set each to zero
x-10=0
x=10

x+1=0
x=-1
false, no negative positions (assuming it didn't go backwards)

x=10
sub into a function
y=-x+10
y=-10+10
y=0

yes they intersect at (10,0), or at 10 feet to the right and 0 feet up
adioabiola

Yes, the two objects interest (intersect) and they do so at times; t = 1 and t = 10

At the point when the objects; (rocket and flare) interest, they are at the same position, y.

  • y(rocket) = y(flare)

  • y(rocket) = -x² + 10x

  • y(flare) = -x + 10

Therefore,

  • -x² + 10x = -x + 10

  • -x² + 11x - 10 = 0

x² -11x +10 = 0

By solving quadratically;

  • x² -10x - x + 10 = 0

x = 10 OR x = 1

Therefore, the two objects interest and they do so at times, t = 1 and t= 10

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