### 8. Self Study Problems

#### Problem (1)

PVI station and location are 74+26.50 and 772.30 ft. What are the endpoints' stations and elevations of a 750.00 ft long curve with incoming and outgoing grades of -4.00% and +2.00%?

#### Problem (2)

PVI station and location are 56+50.00 and 1325.00 ft. Incoming and outgoing grades are +5.0% and -3.5%. A 500.00 ft long vertical curve will be used.

#### Problem (3)

A 425.00 ft long curve ends at station and elevation 88+00.00 and 1220.00. Its initial and final grades are -4.00% and +2.75%.

#### Problem (4)

A curve begins at station 32+00.00 and elevation 912.00 ft; it ends at station 38+00.00 and elevation 915.00 ft. The PVI elevation is 918.00 ft.

#### Problem (5)

A 400.00 ft vertical curve begins at station 29+00.00 and elevation 954.00 ft. Its initial and final grades are -1.00% and -2.25%.

##### Part (a)

What are the station and elevation of the curve's midpoint?

##### Part (b)

What are the stations and elevations of the curve's highest and lowest points?

#### Problem (6)

PVI station and elevation are 41+00.00 and 1262.00 ft. Incoming and outgoing grades are -2.50% and +3.00%. What is the curve length if it must pass through an elevation of 1268.00 ft at station 42+50.00?

#### Problem (7)

A +1.75% grade intersects a -2.25% grade at 32+50.00 and elevation 1015.00. An existing overpass is located at station 31+56.50. Its underside elevation is 1022.50 ft. What is the minimum curve length which will provide 12 ft of clearance under the overpass?