As a speeding train crosses a trestle over a deep gorge,a child drops his toy plane from the window.The path of the toy plane is modeled by $x ^ { 2 } = - 6.0 ( y - 110 )$ ,where y is the height above the floor of the gorge and distances are measured in feet.How far will the toy plane travel horizontally before it hits the bottom of the gorge? [Note: The toy plane does not glide;it "drops like a rock."]
A)6.0 ft
B)10 ft
C)25.7 ft
D)110 ft
E)660.0 ft

Question

Quizplus · Accepted Answer

The equation given is $x^2 = -6.0(y - 110)$. To find the horizontal distance when the toy hits the bottom of the gorge, set $y = 0$ (the bottom of the gorge). Substituting $y = 0$ into the equation gives $x^2 = -6.0(0 - 110) = 660$. Taking the square root of both sides gives $x = \sqrt{660}$, which is approximately 25.7 feet.

As a Speeding Train Crosses a Trestle Over a Deep x2=−6.0(y−110)x ^ { 2 } = - 6.0 ( y - 110 )x2=−6.0(y−110)

As a Speeding Train Crosses a Trestle Over a Deep $x ^ { 2 } = - 6.0 ( y - 110 )$