Question

rain is falling in vertically downward direction with speed 10√3 km/h. if wind is blowing in eastward direction with speed 10km/h, then the velocity of rain observed by a person standing on the ground is
a. 20km/h
b. 10km/h
c. 10√3km/h
d. 10(√3-1)km/h

Please answer fast.​

Answer 1

Given:

Speed of the rain falling vertically = 10√3 km/hr

Speed of wind blowing in eastward direction = 10 km/hr

To find:

The velocity of rain observed by a person standing on the ground.

Solution:

The resultant velocity of wind will be observed by the person standing on the ground.

Speed of wind = -10√3 j km/hr

Speed of wind = 10 i km/hr

Magnitude of resultant velocity |v| = √(-10√3)²+(10)² = 20 km/hr

Angle made by resultant velocity from horizontal (+ve x axis):

tanα= -10√3/10 = -√3 = -60°

Velocity of rain = 20 cos(-60)°i - 20 sin (60)° j

= 10 i - 10√3j km/hr

Therefore the velocity of rain as observed by the person is 10i - 10√3j km/hr.