Home
Class 12
PHYSICS
A stationary person observes that rain i...

A stationary person observes that rain is falling vertically down at `30 km h^-1`. A cyclist is moving up on an inclined plane making an angle `30^@` with horizontal at `10 km h^-1`. In which direction should the cyclist hold his umbrella to prevent himself from the rain ?

A

At an angle `tan^(-1)(3sqrt(3))/(5)` with inclined plane

B

At an angle `tan^(-1) (3 sqrt(3))/(5)` with horizontal

C

At an `tan^(-1)(sqrt(3))/(7)` with inclined plane

D

At an angle `tan^(-1)(sqrt(3))/(7)` with vertical

Text Solution

Verified by Experts

The correct Answer is:
ad
`overset(rarr)v_(R)//G =- 30 hat j v_(M//G)=(10sqrt(3))/(2)+(10)/(2)hatj`
`tan theta =(5sqrt(3))/(35)=sqrt(3)/(7)`
angle of `V_(R)/M` with inclined plane is `60 - theta =beta tan beta = tan (60-theta)`
`=(tan 60^(@) - tan theta)/(1+tan 60^(@) tan theta)`

`rarr beta \ tan^(-1) (3sqrt(3))/(5)`
Promotional Banner

Similar Questions

Explore conceptually related problems

A stationary person observes that rain is falling vertically down at 30 km//hr . A cyclist is moving up on an inclined plane making an angle 30^(@) with horizontal at 10 km//hr . In which direction should the cyclist hold his umbrella to prevent himself from the rain ?

Rain is falling vertically with a speed of 35 ms^(-1) . Winds starts blowing after sometime with the speeds of 12ms^(-1) in east to west direction. At what angles with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?

Rain is falling vertically with a velocity of 25 ms^-1 . A woman rides a bicycle with a speed of 10 ms^-1 in the north to south direction. What is the direction (angle with vertical) in which she should hold her umbrella to safe herself from rain ?

A man is walking on a level road at a speed of 3.2 km^(-1) . Rain drops fall vertically with a speed of 4.0 km h^(-1) . Find the velocity of the raindrops with respect to the man. In which direction, the man should hold his umbrella to protect himself from rain ?

Rain is falling, vertically with a speed of 1m//s .Wind starts blowing after sometime with a speed of 1.732 m//s in east to west direction. In which direction should a boy waiting at a bus stop hold his umbrella?

Rain is falling with a speed of 4nVs inadirection making an angle of 30^(@) with vertical towards south. What should be the magnitude & direction of velocity of cyclist to hold his umbrella exactly vertical, so that rain does not wet him:

A man walking on a road with a velocity of 5 km per hour encounters rain falling vertically with a velocity of 25 km per hour. At what angle should he holds his umbrella in order to protect himself form the rain?

Rain is falling vertically downwards with a speed of 4 km h^-1 . A girl moves on a straight road with a velocity of 3 km h^-1 . The apparent velocity of rain with respect to the girl is.

Rain is falling vertically and a man is moving with velocity 6 m s^-1 . Find the angle at which the man should hold his umbrella to aboved getting wet.