Question

A pipe which can rotate in a vertical plane is mounted on a cart. The
cart moves uniformly along a horizontal path with a speed
V1 = 2 m/s. At what angle a to the horizontal should the pipe be
placed so that drops of rain falling vertically with a velocity V2 = 6m/s
move parallel to the axis of the pipe without touching its walls?
Consider the velocity of the drops as constant due to the resistance of
the air.​

Answer 1

Explanation:

By relative velocity

velociry (w.r.t.c.)=-2 î-6j

tan a =-6 /-3

Answer 2

Answer:

Explanation:

Speed of the cart = v1 = 2m/s. (Given)

Velocity of drops of the rain = v2 = 6m/s.  (Given)

Horizontal component of velocity = v1 = v2 Cos Ф

By the concept of relative velocity,

Thus, substituting the values in the equation -  

Ф = cos~-1 (v1/v2)

= cos~-1 (2/6)

= cos~-1 (1/3)

= 70.5°

Thus, the angle to which the horizontal pipe be placed so that the drops of rain falling vertically with a velocity and move parallel to the axis of the pipe without touching it's walls should be 70.5°.