Question

In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato. The other potatoes are arranged 3 m apart in a straight line, with a total of 10 potatoes, as shown in the figure: A competitor starts from the bucket, picks up the nearest potato, runs back to the bucket to drop it in, then returns to pick up the next potato. This process continues until all the potatoes are in the bucket.

Based on the above information, answer the following questions:

1. What is the distance covered to pick up the first potato and drop it in bucket?    1
2. What is the distance covered to pick up the second potato and drop it in bucket?    1
3. 1. What is the total distance the competitor has to run?    2
      OR
   2. If average speed of competitor is 5 m/s, then find the average time taken by competitor to put all the potatoes in the bucket.    2

Answer 1

(i) The competitor starts at the bucket, runs 5 m to the first potato, and runs 5 m back to drop it in the bucket.

Distance = 2 × 5

= 10 m

(ii) The second potato is 3 m further than the first, making it 5 + 3 = 8 m from the bucket. The competitor runs to it and back.

Distance = 2 × (5 + 3)

= 2 × 8

= 16 m

(iii) (a) The distances for each potato form an Arithmetic Progression (A.P.): 10, 16, 22, .....

First term (a) = 10 m

Common difference (d) = 16 − 10

= 6 m

Number of terms (n) = 10 

Using the sum formula `S_n = n/2[2a + (n - 1)d]`

= `10/2[2(10) + (10 - 1)6]`

= 5[20 + (60 − 6)]

= 5[20 + 54]

= 5 × 74

= 370 m

OR

(b) If the competitor’s average speed is 5 m/s, the time taken is:

Time = `"Total Distance"/"Average Speed"`

= `370/5`

= 74 sec