Question

10 point A bridge with a supporting parabolic arch spans 60 ft with a 30ft wide road passing underneath the bridge. How high must the arch be in order to have a minimum clearance of 13 ft above the road? 60 30 Round your final answer to 1 decimal place type your answer f

Answer 1

here answer is 17.3 feet

picture for this parabolic arch with orgin as center of road is 41513) (-30,0) (0.0 (150) (30,0) It wil) arch is 6o. So total length of be 30 feet from center to both side. we know equation of a parabola having 96 Intercept at X=m and 2 X=D ?S y = a (x-m) (x-4) this pansbola has x intercept at (+30,0) and (30,0) So equetion is y = a (x-30) (x+30) mg clearence should be 13 feet above road So at a distance = 15 g should be 13. and find a value of constant a 13= a (15-30) (15+30) apply this

13 = a X-675 13 =-0.01925926 -675 so equshion of this arch is a= y = -0.01925 926 OC-30) (C+30) heigh of arch is y Is y value when Y=0. so height is y = -0.01925926 (0-30) (0+30) = -0.0192 5926x 900 17.3333 17.3 so heigh 17.3 of bridge should be Feet 0,1703) (1818) (15,13) -30% 0.0 (-300 (300) - GO