Question 175: Motion in 2D & Vectors

Question

A ship A is moving Westwards with a speed of 10 km h$$-$$1 and a ship B 100 km South of A, is moving Northwards with a speed of 10 km h$$-$$1. The time after which the distance between them becomes shortest, is

Accepted Answer

$${\overrightarrow V _A} = 10\left( { - \widehat i} \right)$$
$${\overrightarrow V _B} = 10\left( {\widehat j} \right)$$
$${\overrightarrow V _{BA}} = {\rm{10}}\widehat {\rm{j}}{\rm{  +  10}}\widehat i{\rm{ = 10}}\sqrt 2 \,{\rm{km/h }}$$
Distance OB = 100 cos 45ÃÂ° = 50$$\sqrt 2 $$ km
Time taken to reach the shortest distance between
A and B = $${{OB} \over {\overrightarrow {{V_{BA}}} }} = {{50\sqrt 2 } \over {10\sqrt 2 }} = 5h$$

Answer

$$5\sqrt 2 $$ h

Answer

$$10\sqrt 2 $$ h

Answer

0 h

Answer

5 h

Motion in 2D & Vectors

A ship A is moving Westwards with a speed of 10 km h$-1 and a ship B 100 km South of A, is moving Northwards with a speed of 10 km h-$1. The time after which the distance between them becomes shortest, is

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