TS EAMCET · Maths · Vector Algebra
Two ships leave a port at the same time. One of them moves in the direction of \(\mathrm{E} 50^{\circ} \mathrm{N}\) with a speed of 8 kmph and the other moves in the direction of \(\mathrm{S} 20^{\circ} \mathrm{E}\) with a speed of 12 kmph. Then the distance between the ships at the end of 2 hours is (in km )
- A \(8 \sqrt{7}\)
- B 34
- C \(8 \sqrt{19}\)
- D 32
Answer & Solution
Correct Answer
(C) \(8 \sqrt{19}\)
Step-by-step Solution
Detailed explanation
\(d_1 = 8 \times 2 = 16 \text{ km}\) \(d_2 = 12 \times 2 = 24 \text{ km}\) \(\text{Angle between directions } \phi = 50^\circ (\text{N of E}) + 70^\circ (\text{S of E}) = 120^\circ\) \(D^2 = d_1^2 + d_2^2 - 2 d_1 d_2 \cos \phi\) \(D^2 = 16^2 + 24^2 - 2(16)(24) \cos 120^\circ\)…
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