the discus throw is an event in which an athlete attempts

Case Study 1:- the discus throw is an event in which an athlete attempts to throw a discus. The sthlete spins anti-clockwise around one and half times through a circle, then releases the throw. When released, the discus travels along tangent to the circular spin orbit.

In the given figure, AB is one such tangent to a circle of radius 75 cm. Point O is centre and ∠ABO = 30°. PQ is parallel to OA.

Based on above information :

(a) Find the length of AB. 1

(b) Find the length of OB. 1

(c) Find the length of AP. 2

Find the length of PQ. 2

Solution:-

(a) In ΔOAB

$\tan 30 = \dfrac{OA}{AB}$

⇒ $\dfrac{1}{\sqrt{3}} = \dfrac{75}{AB}$

⇒ AB = 75√3 cm

(b) In ΔOAB

$\sin 30 = \dfrac{OA}{OB}$

⇒ $\dfrac{1}{2} = \dfrac{75}{OB}$

⇒ $OB = 150$ cm

(c) OB = 150 cm

Radius OQ = 75 cm

Hence, QB = 150 – 75 = 75 cm

Since OA ll QP

In ΔQPB

$\cos 30 = \dfrac{BP}{BQ}$

⇒ $\dfrac{\sqrt{3}}{2} = \dfrac{BP}{75}$

⇒ $BP = \dfrac{75\sqrt{3}}{2}$

Now, AP = AB – PB

⇒ $AP = 75\sqrt{3} - \dfrac{75\sqrt{3}}{2}$

⇒ $AP = \dfrac{75\sqrt{3}}{2}$ cm

In ΔQPB

$\sin 30 = \dfrac{QP}{QB}$

⇒ $\dfrac{1}{2} = \dfrac{QP}{75}$

⇒ $QP = \dfrac{75}{2} = 37.5$ cm

CAse Study 2:- While designing the school year book, a teacher asked the student that the length and width of a particular photo is increased by x units each to double the area of the photo. The original photo is 18 cm long and 12 cm wide.

Based on the above information, answer the following questions:

(i) Write an algebraic equation depicting the above information. 1

(ii) Write the corresponding quadratic equation in standard form. 1

(iii) What should be the new dimensions of the enlarged photo ? 2

Can any rational value of x make the new area equal to 220 cm² ?

Case Study 3:- India meteorological department observes seasonal and annual rainfall every year in different sub-divisions of our country.

It helps them to compare and analyse the results. The table given below shows sub-division wise seasonal (monsoon) rainfall (mm) in 2018 :

Based on the above information, answer the following questions:

(i) Write the modal class. 1

(ii) Find the median of the given data. 2

Find the mean rainfall in this season.

(iii) If sub-division having at least 1000 mm rainfall during monsoon season, is considered good rainfall sub-division, then how many sub-division had good rainfall ? 1

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