First slide

Motion in a plane

Question

A Ship ‘A’ streams due north at a speed of 8 kmph and ship B due west at a speed of 6 kmph. The velocity of A w.r.t. B is.

Moderate

A

10 kmph, Tan^–1(4/3) N of E
B

10 kmph, Tan^–1(4/3) E of N
C

10 kmph NE
D

2 kmph, Tan^–1(4/3) N of E

Solution

$\large {\overline V _{AB}} = {\overline V _A} - {\overline V _B};{\overline V _A} = 8\widehat j,\,\,{\overline V _B} = - 6\widehat i$
$\large {\overline V _{AB}} = {\overline V _A} - {\overline V _B} = 8\widehat j + 6\widehat i$
$\large \left| {{{\overline V }_{AB}}} \right| = 10kmph$
$\large Tan\theta = \frac{8}{6} = \frac{4}{3}$
$\large \theta = Ta{n^{ - 1}}\left( {\frac{4}{3}} \right)along N\,of\,E$

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