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Q.

A swimmer is approaching the shore with a speed of 53ms−1. At the instant when it is at a distance of 303m from the shore, he projects a ball at an elevation of 30° for it to just reach the shore. The speed of stone relative to swimmer is 5x ms−1. Find the value of x.

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answer is 4.

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Detailed Solution

Here, ux=53+urel cos⁡30∘and uy=urel sin⁡30∘∴ 303=53+urelcos⁡30∘Tand T=2uyg=2urelsin⁡30∘g=urelg∵ 303=53urelg+32gurel2⇒ 300=5urel +urel 22⇒ urel22+5urel−300=0⇒ urel2+10urel−600=0∴ urel=−10±100+24002=−10±502=402=20ms−1∴ n=4
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