Question

Manpreet Kaur is the national record holder for women in the shot-put discipline. Her throw of 18.86m at the Asian Grand Prix in 2017 is the maximum distance for an Indian female athlete. Keeping her as a role model, Sanjitha is determined to earn gold in Olympics one day. Initially her throw reached 7.56m only. Being an athlete in school, she regularly practiced both in the mornings and in the evenings and was able to improve the distance by 9cm every week. During the special camp for 15 days, she started with 40 throws and every day kept increasing the number of throws by 12 to achieve this remarkable progress.

1. How many throws Sanjitha practiced on 11^th day of the camp?
2. What would be Sanjitha’s throw distance at the end of 6 weeks?
   (or)
   When will she be able to achieve a throw of 11.16 m?
3. How many throws did she do during the entire camp of 15 days?

Answer 1

i. Number of throws during camp. a = 40; d = 12

t₁₁ = a + 10d

= 40 + 10 × 12

= 160 throws

ii. a = 7.56 m; d = 9 cm = 0.09 m

n = 6 weeks

t_n = a + 6d

= 7.56 + 6(0.09)

= 7.56 + 0.54

Sanjitha’s throw distance at the end of 6 weeks = 8.1 m

(or)

a = 7.56 m; d = 9 cm = 0.09 m

t_n = 11.16 m

t_n = a + (n – 1) d

11.16 = 7.56 + (n – 1) (0.09)

3.6 = (n – 1) (0.09)

n – 1 = `3.6/0.09` = 40

n = 41

Sanjitha’s will be able to throw 11.16 m in 41 weeks.

iii. a = 40; d = 12; n = 15

S_n = `n/2[2a + (n - 1)d]`

S_n = `15/2[2(40) + (15 - 1) (12)]`

= `15/2[80 + 168]`

= `15/2[248]`

= 1860 throws