Question

Rain is falling vertically with a speed of 35 m/s. Winds start blowing after sometime with a speed of 12m/s in east to west direction. In which direction should a boy waiting at a bus stop hold his umbrella ?

• A. ${19}^0$ inclination to vertical
• B. ${19}^0$ inclination to horizontal
• C. ${71}^0$ inclination to vertical
• D. ${71}^0$ inclination to Horizontal

Answer 1

Answer: (A), (D)

The correct options are
A ${19}^0$ inclination to vertical
D ${71}^0$ inclination to Horizontal

Given,

speed of rain is $35m/s$

Speed of wind is $12m/s$

The resultant velocity of raindrops will be the vector sum of the raindrop speed (vertical) and the horizontal wind speed.

The magnitude of the resultant velocity of the raindrops is:

$\sqrt{({12}^2+{35}^2)}=37m/sec$

the direction of the resultant velocity vector with the vertical

$=ta{n}^{-1}\left(\frac{12}{35}\right)={19}^0.$

The umbrella should be pointed in the direction opposite to the resultant velocity of the raindrops. So it should be in the direction ${19}^0$. the inclination to the vertical opposite to the direction of wind., towards East.

Or ${71}^0$ with the Horizontal direction (east) towards vertical