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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.
Based on above information, answer the following questions using Arithmetic Progression :
(i) Find the distance of $10^{th}$ pole from the base.
(ii) Find the distance between $15^{th}$ pole and $25^{th}$ pole.
(iii) (a) Find the time taken by cable car to reach $15^{th}$ 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.
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.
Based on above information, answer the following questions using Arithmetic Progression :
(i) Find the distance of $10^{th}$ pole from the base.
(ii) Find the distance between $15^{th}$ pole and $25^{th}$ pole.
(iii) (a) Find the time taken by cable car to reach $15^{th}$ 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.
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AP formed is $200, 350, 500, ...$
(i) Distance of $10^{th}$ pole from base = $A_{10}$
$= 200+9\times 150$
$= 1550$ m
(ii) Distance between $15^{th}$ pole and $25^{th}$ pole = $a_{25} - A_{15}$
$= 10 \times 150 = 1500$ m
(iii) (a) Distance of $15^{th}$ pole from the top = $300 + 14 \times 150$
$= 2400$ m
Time taken by cable car = $\frac{2400}{5} = 480$ seconds or $8$ minutes
OR
(iii) (b) Distance of last pole from the base = $(5000 – 300)$ m = $4700$ m
$\therefore a_n = 4700$
$\Rightarrow 200+ (n – 1)150 = 4700$
Solving, we get $n = 31$
(i) Distance of $10^{th}$ pole from base = $A_{10}$
$= 200+9\times 150$
$= 1550$ m
(ii) Distance between $15^{th}$ pole and $25^{th}$ pole = $a_{25} - A_{15}$
$= 10 \times 150 = 1500$ m
(iii) (a) Distance of $15^{th}$ pole from the top = $300 + 14 \times 150$
$= 2400$ m
Time taken by cable car = $\frac{2400}{5} = 480$ seconds or $8$ minutes
OR
(iii) (b) Distance of last pole from the base = $(5000 – 300)$ m = $4700$ m
$\therefore a_n = 4700$
$\Rightarrow 200+ (n – 1)150 = 4700$
Solving, we get $n = 31$