Question

Manpreet kaur is the national record holder for women in the shot-put discipline. Her throw of 18.86 m 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 7.56 m 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 9 cm every week. During the special camp for 15 days, she started with 40 throws, and every day she kept increasing the number of throws by 12 to achieve this remarkable progress.

Based on the above information, answer the following questions.

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

Answer 1

From the problem statement, two different APs are described:

Daily Throws during Camp:

First term, \[a = 40\]

Common difference, \[d = 12\]

Weekly Throw Distance Improvement:

Initial distance, \[A = 7.56\text{ m}\]

Improvement per week, \[D = 9\text{ cm} = 0.09\text{ m}\]

i. Number of throws practiced on the 11th day of camp:

Formula: \[T_n = a + (n - 1)d\]

Calculation: \[T_{11} = 40 + (11 - 1) \times 12\]

\[T_{11} = 40 + 10 \times 12\]

\[= 40 + 120\]

\[= 160\]

She practiced 160 throws on the 11th day.

ii. Sanjitha’s throw distance at the end of 6 weeks:

Distance after 6 weeks is the initial throw plus 6 weekly improvements:

\[\text{Distance} = A + 6 \times D\] 

\[\text{Distance} = 7.56\text{ m} + 6 \times 0.09\text{ m}\] 

\[\text{Distance} = 7.56\text{ m} + 0.54\text{ m} = 8.1\text{ m}\]

Her throw distance at the end of 6 weeks will be 8.1 m.

iii. When she will achieve a throw of 11.16 m:

Let the target distance be achieved after n weeks: \[7.56 + n \times 0.09 = 11.16\] 

\[0.09n = 11.16 - 7.56\] 

\[0.09n = 3.60\] 

\[n = \frac{3.60}{0.09} = 40\text{ weeks}\] 

If counting by terms of AP where \(T_n = A + (n - 1)D = 11.16\), then \((n - 1) = 40 \Rightarrow n = 41\) weeks.

She will achieve it after 41 weeks or 40 weeks of improvements.

iv. Total throws made during the entire camp of 15 days:

Formula: \[S_n = \frac{n}{2}[2a + (n - 1)d]\]

Substitution and Calculation:

For \[n = 15, a = 40, d = 12\]: 

\[S_{15} = \frac{15}{2}[2(40) + (15 - 1)12]\] 

\[S_{15} = \frac{15}{2}[80 + 14 \times 12]\] 

\[S_{15} = \frac{15}{2}[80 + 168] = \frac{15}{2} \times 248\] 

\[S_{15} = 15 \times 124 = 1860\]

She made a total of 1860 throws during the entire camp.