The discus throw is an event in which an athlete attempts to throw a discus. The athlete spins anti-clockwise around one and a half times through a circle, then releases the throw. When released, the

Question

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

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

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Based on above information:
(a) Find the length of $AB$.
(b) Find the length of $OB$.
(c) Find the length of $AP$.

OR

(c) Find the length of $PQ$.

Accepted Answer

Step 1: (i) $	an 30° = \frac{1}{\sqrt{3}} = \frac{75}{AB}$
$\Rightarrow AB = 75\sqrt{3}$ cm
Step 2: (ii) $\sin 30° = \frac{1}{2} = \frac{75}{OB}$
$\Rightarrow OB = 150$ cm
Step 3: (iii) $QB = 150 - 75 = 75$ cm
$\Rightarrow Q$ is mid point of $OB$
Since $PQ \parallel AO$ therefore $P$ is mid point of $AB$
Hence $AP = \frac{75\sqrt{3}}{2}$ cm.

Question

Solution