Heights and Distances Practice Test 1

Question : 13 of 40

Marks: +1, -0

Two ships leave a port at the same instant. One sails at 30 km/hr in the direction N 32°E while the other sails at 20 km/hr in the direction S 58° E. After two hours the ships are distant from each other by:

$15 √6$ km
36.5 km
$20√ 13$ km
100 km

Validate

Solution:

Let two ships started from point O at the speed of 30 km/hr 0 and 20 km/hr respectively, after two hours they reach at points A and B.
Now, ∠ NOA = 32° and ∠ SOB = 58°,
Then, ∠ AOB = 180° – (32° + 58°) = 90°
Since Δ AOB is a right triangle in which OA = 2 × 30 = 60 km and OB = 2 × 20 = 40 km
Since,

AB=√{OA^2+OB^2}

=√{60^2+40^2}=20√13\km

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