First slide

Vectors

Question

Rain is falling vertically with a speed of 4 m $s^{- 1}$ . Wind starts blowing after sometime with a speed of 3 m $s^{- 1}$ in east to west direction. In which direction should a boy waiting at a bus stop hold his umbrella

Moderate

A

37° with the vertical towards west
B

53° with the vertical towards east
C

37° with the vertical towards east
D

53° with the vertical towards west

Solution

$\overset{⇀}{V_{R M}} = - 4 \overset{⏞}{k} - 3 \overset{⏞}{i}$ $(\overset{⇀}{V_{R M}} = \overset{⇀}{V_{R}} + \overset{⇀}{V_{W}})$
taking east along $\overset{⏞}{i}$ north along $\overset{⏞}{j}$ and vertically up along $\overset{⏞}{k}$ $\tan θ = \frac{3}{4} = 37^{0} w i t h t h e v e r t i c a l t o w a r d s e a s t$

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