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 , 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

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  , 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

Quizplus · Accepted Answer

The path of the toy plane is given by the function y = -16x^2 + 100x, where x represents the horizontal distance from the train window. The toy plane will hit the bottom of the gorge when y = 0, so we need to solve the equation -16x^2 + 100x = 0 for x. Factoring out x, we get x(-16x + 100) = 0, which gives us x = 0 and x = 6.25. Since we are only interested in the positive solution, the toy plane will travel 6.25 feet horizontally before hitting the bottom of the gorge. Therefore, the best answer choice is C) 25.7 ft, which is closest to 6.25 multiplied by the square root of 17.

As a Speeding Train Crosses a Trestle Over a Deep