The vertical angle of the top of the flagpole as observed from point A is equal to 60°, and that of the bottom of the flagpole is 52°. The flagpole is placed on top of a pedestal. If the distance from A to the base of the pedestal is 14.20m.
1 Find the height of the pedestal
2 Find the height of the flagpole on top of the pedestal.
3 Find the distance from A to the top of the flagpole.
Solution:
It is estimated that between the hours of noon and 7:00 P.M. the speed of a highway traffic flowing past the intersection of EDSA and Ortigas Avenue in approximately
S = t3 – 9t2 +15t + 45 kph
Where “t” is the number of hours past noon.
1 At what time between noon and 7:00 P.M. is the traffic moving the fastest.
2 At what time between noon and 7:00 P.M. is the traffic moving the slowest.
3 What is the slowest speed it is moving at this time.
Solution:
The equilateral hyperbola xy = 8 has the x-axis and y-axis as asymptote.
1 Determine the distance between the vertices.
2 Compute the length of the conjugate axis.
3 Compute the eccentricity of the hyperbola.
Solution:
For a nominal rate of 6% compounded semi-quarterly for 8years in an ordinary annuity, compute the following
1 Sinking fund factor.
2 Present worth factor.
3 Capital recovery factor.
Solution:
An ellipse has an equation of 9x2 + 16y2 = 144.
1 If the area enclosed by the ellipse on the first and 2nd quadrant is revolved about ***the x-axis, what is the volume generated.
2 What is the length of arc in the first quadrant of an ellipse.
3 What is the equation of the diameter of the ellipse which bisect all chords having a ***slope of 2.
Solution:
Compute the interest for an amount of P200,000 for a period of 8 yrs.
1 If it was made at a simple interest rate of 16%.
2 If it was made at 16% compounded bi-monthly.
3 If it was made at 16% compounded continuously.
Solution:
Given the technical description of a triangular lot.
LINES BEARING DISTANCE
AB N. 40° W. ?
BC N. 60° E. 810 m.
CA Due South ?
An area of 190,000 m2 is to be segregated along the side BC starting from B.
1 Compute the location of the other end of the dividing line BD along the side CA ***measured from C.
2 Compute the length of the diving line.
3 Compute the bearing of the dividing line from B.
Solution:
An easement curve has a length of spiral equal to 60m. having a central curve of a radius of 400m. The design velocity of the car allowed to pass thru this portion is 100kph.
1 Compute the rate of increase of centripetal acceleration.
2 If the friction factor is equal to 0.14, compute the super elevation rate in m/m ***width of roadway.
3 Compute the width of one lane of roadway if the difference in grade between the ***centerline and the edge of the roadway is 1/220.
Solution:
The peak hour factor for traffic during rush hour is equal to 0.60 with a highest 5min. volume of 250 vehicles. The space mean speed of the traffic is 90 kph.
1 Compute the flow of traffic in vehicles/hour.
2 Compute the density of traffic in vehicles/km.
3 Compute the max. spacing of the cars in meters.
Solution:
A line was determined to be 2395.25m. when measured with a 30m. steel tape supported throughout its length under a pull of 4kg at a mean temperature of 35°C. Tape used is of standard length of 20°C under a pull of 5kg. Cross-sectional area of tape is 0.03sq.cm. Coefficient of thermal expansion is 0.0000116°C. Modulus of elasticity of tape is 2 x 106 kg/cm3.
1 Determine the error of the tape due to change in temperature.
2 Determine the error due to tension.
3 Determine the corrected length of the line.
Solution:
The centerline of a proposed road cross section crosses a small valley between station 10 + 022 (elevation 123.00m.) and station 10 + 060 (elevation 122.50m.). The stationing at the bottom of the valley is 10 + 037 (elevation 111.2m.). The grade line of the proposed road passes the ground points at the edges of the valley (sta. 10 + 022) and (10 + 060) and the section at any of these stations are three level sections. Width of road base = 10m. with sideslope of 2:1. Assume that the sides of the valley slope directly to the lowest point from the edges.
1 Find the cross sectional area of fill at station 10 + 037.
2 Compute the volume of fill from station (10 + 022) to (10 + 037)
3 Compute the volume of fill from station (10 + 037) to (10 + 060).
Solution:
The tangents of a simple curve have bearings of N.20°E and N.80°E. respectively. The radius of the curve is 200m.
1 Compute the external distance of the curve.
2 Compute the middle ordinate of the curve.
3 Compute the stationing of point A on the curve having a deflection angle of 6° from ***the P.C. which is at 1 + 200.00.
Solution:
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