A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y=-0.06x^2+9.6x+5.4 where x is the horizonal distance in meters from the starting point on the roof and y is the height, in meters, of the rocket above the ground. How far horizontally from its starting point will the rocket land? Round your answer to the nearest hundredth.

a) 4.30 m
b) 160.56 m
c)160.23 m
d) 13.94 m

Question

A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y=-0.06x^2+9.6x+5.4 where x is the horizonal distance in meters from the starting point on the roof and y  is the height, in meters, of the rocket above the ground.  How far horizontally from its starting point will the rocket land? Round your answer to the nearest hundredth.

a) 4.30 m
b) 160.56 m
c)160.23 m
d) 13.94 m

anonymous · Answer

I will give a medal, and become a fan!

ranga · Answer

When the rocket lands, y = 0.
Set y = 0 in the given equation and solve for x.

ranga · Answer

0 = -0.06x^2+9.6x+5.4
multiply by -100
0 = 6x^2 - 960x - 540 
divide by 6
x^2 - 160x - 90 = 0
plug the numbers into the quadratic formula and find x.