A circular bend in a road has radius 80m. A vehicle travels along a portion of this bend that subtends an angle of 45∘ at the centre of the circle. Answer the following.
a. (i) Convert 45∘ to radian measure, correct to two decimal places.
b. (ii) Calculate the length of the curved portion of the road that the vehicle covers.
c. (iii) If the vehicle maintains a speed of 54km h−1 while negotiating the bend, determine the time taken, in seconds, to travel this curved portion. (Take π=3.14.)