Question

In a cricket match a batsman hits the ball and a fielder, 30 m away, fails to stop the ball but deflects it and slows it down. The ball comes to rest 20m from where the fielder deflected it. Find the distance from where the ball was hit to where it came to rest. ( Angle between 30m and 20m is 110° )

Answer 1

Answer on Question #51336 - Math - Vector Calculus

In a cricket match a batsman hits the ball and a fielder, $a = 30\mathrm{m}$ away, fails to stop the ball but deflects it and slows it down. The ball comes to rest $b = 20\mathrm{m}$ from where the fielder deflected it. Find the distance $l$ from where the ball was hit to where it came to rest. (Angle between $a$ and $b$ is $\alpha = 110{}^{\circ}$)

**Solution:**

According to the law of cosines,

$$l ^ {2} = a ^ {2} + b ^ {2} - 2 a b \cos \alpha$$ $$l = \sqrt {a ^ {2} + b ^ {2} - 2 a b \cos \alpha} = \sqrt {9 0 0 \mathrm {m} ^ {2} + 4 0 0 \mathrm {m} ^ {2} - 1 2 0 0 \mathrm {m} ^ {2} \cos 1 1 0 {}^ {\circ}} = 4 1. 3 6 \mathrm {m}$$

**Answer:** $l = \sqrt{a^2 + b^2 - 2ab\cos\alpha} = 41.36\mathrm{m}$

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