A superhero is trying to leap over a tall building. The function f(x)=-16x^2+200x gives the superheroes height in feet as a function of time. The building is 612 feet high. Will the superhero make it over the building? Explain.
Thank you
well, the max height is found at (6.25,625)
So, as long as he's not too far away when he tries to leap over the building, yes, he'll make it (as long as the building is sufficiently narrow).
A stone is thrown straight up, with an initial velocity of 20 meters per second and from an initial height of 2 meters. The height h of the stone after t seconds is described by the function: h(t) = 2 + 20t - 4.9t2. What is the stone’s average speed during the first two seconds of its flight?
To determine if the superhero will make it over the building, we need to find the maximum height of the superhero's leap.
The given function f(x) = -16x^2 + 200x represents the height of the superhero at time x. The term -16x^2 represents the effects of gravity on the superhero's height, while the term 200x represents the initial upward velocity of the leap.
To find the maximum height, we need to find the vertex of the parabola represented by the function f(x). The vertex of a parabola with equation f(x) = ax^2 + bx + c has x-coordinate given by x = -b / (2a). In this case, a = -16 and b = 200, so the x-coordinate of the vertex is x = -200 / (2(-16)) = -200 / -32 = 6.25.
Now, to find the maximum height, we substitute this x-coordinate into the original function.
f(6.25) = -16(6.25)^2 + 200(6.25) = -16(39.0625) + 1250 = -625 + 1250 = 625 feet.
The maximum height the superhero reaches is 625 feet.
Since the height of the building is 612 feet, and the superhero reaches a maximum height of 625 feet, we can conclude that the superhero will indeed make it over the building.