To the captain of a ship A travelling with velocity vA→ = (3i^-4j^) km/h, a second ship B appears to have a velocity (5i^ +12j^) km/h. What is the true velocity of the ship B?

vB→ = vBA→+vA→ = (5i^+12j^) +(3i^-4j^)vB→ = 8i^+8j^

To the captain of a ship A travelling with velocity vA→ = (3i^-4j^) km/h, a second ship B appears to have a velocity (5i^ +12j^) km/h. What is the true velocity of the ship B?

vB→ = vBA→+vA→ = (5i^+12j^) +(3i^-4j^)vB→ = 8i^+8j^

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To the captain of a ship A travelling with velocity $\vec{v_{A}} = (3 \hat{i} - 4 \hat{j})$ km/h, a second ship B appears to have a velocity (5 $\hat{i} + 12 \hat{j}$ ) km/h. What is the true velocity of the ship B?

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$- 2 \hat{i} - 16 \hat{j} km / h$

$2 \hat{i} + 16 \hat{j} km / h$

$8 (\hat{i} + \hat{j}) km / h$

$13 \hat{i} + 8 \hat{j} km / h$

answer is D.

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Detailed Solution

$\vec{v_{B}} = \vec{v_{BA}} + \vec{v_{A}}$

= $(5 \hat{i} + 12 \hat{j}) + (3 \hat{i} - 4 \hat{j})$

$\vec{v_{B}} = 8 \hat{i} + 8 \hat{j}$

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To the captain of a ship A travelling with velocity vA→ = (3i^-4j^) km/h, a second ship B appears to have a velocity (5i^ +12j^) km/h. What is the true velocity of the ship B?

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To the captain of a ship A travelling with velocity $\vec{v_{A}} = (3 \hat{i} - 4 \hat{j})$ km/h, a second ship B appears to have a velocity (5 $\hat{i} + 12 \hat{j}$ ) km/h. What is the true velocity of the ship B?