A straight road rises at an inclination of 0.3 radian from the horizontal. Find the slope and change in elevation over a one-mile section of the road.

 

1) A straight road rises at an inclination of 0.3 radian from the horizontal. Find the slope and change in elevation over a one-mile section of the road.

2) In order to allow rain to run off of a road, they are often designed with parabolic surfaces in mind. Suppose a road is 32 feet wide and 0.4 foot higher in the center than it is on the side

a) Write an equation of the parabola with its vertex at the origin
that models the road surface.

b) How far from the center of the road is the road surface 0.2 feet
lower than the center?

3. A parabolic archway is 12 meters high at the vertex. At a height of 10 meters, the width of the archway is 8 meters. How wide is the archway at ground level?

4) Halley’s comet follows an elliptical orbit with the sun as one of the foci. The eccentricity of the orbit is approximately 0.967. The length of the major axis of the orbit is approximately 35.88 astronomical units. (An astronomical unit is about 93 million miles.

(a) Find an equation of the orbit. Let the origin represent the sun and
use the x axis as the major axis.

(b) Find the greatest and least distances (the aphelion and perihelion,
respectively) from the sun’s center to the comet’s center.

5) You and a friend live 4 miles apart. You hear the sound of thunder 18 seconds before your friend hears it. Assuming sound travels at 1100 feet
per second, determine where the lightning occur?