Cable cars at hill stations are one of the major tourist attractions. On a hill station, the length of cable car ride from base point to top most point on the hill is 5000 m. Poles are installed at eq

Question

Cable cars at hill stations are one of the major tourist attractions. On a hill station, the length of cable car ride from base point to top most point on the hill is 5000 m. Poles are installed at equal intervals on the way to provide support to the cables on which car moves.

The distance of first pole from base point is 200 m and subsequent poles are installed at equal interval of 150 m. Further, the distance of last pole from the top is 300 m.

[IMAGE_1]

Based on above information, answer the following questions using Arithmetic Progression:
(i) Find the distance of $10^{	ext{th}}$ pole from the base.
(ii) Find the distance between $15^{	ext{th}}$ pole and $25^{	ext{th}}$ pole.
(iii) (a) Find the time taken by cable car to reach $15^{	ext{th}}$ pole from the top if it is moving at the speed of 5 m/sec and coming from top.

OR

(iii) (b) Find the total number of poles installed along the entire journey.

Accepted Answer

Step 1: (i) AP formed is $200, 350, 500, ...$
Distance of $10^{	ext{th}}$ pole from base $= a_{10} = 200 + 9 	imes 150 = 1550$ m
Step 2: (ii) Distance between $15^{	ext{th}}$ pole and $25^{	ext{th}}$ pole $= a_{25} - a_{15} = 10 	imes 150 = 1500$ m
Step 3: (iii)(a) Distance of $15^{	ext{th}}$ pole from top $= 300 + 14 	imes 150 = 2400$ m
Time taken by cable car $= \frac{2400}{5} = 480$ seconds or $8$ minutes

Question

Solution