Home
Class 11
PHYSICS
A man running on the horizontal road at ...

A man running on the horizontal road at ` 8 km h^(-1)` find the rain appears to be falling vertically. He incresases his speed to `12 km h^(-1)` and find that the drops make angle ` 30^2` with the vertical. Fin dthe speed and direction of the rain with respedt to the road.

Text Solution

Verified by Experts

We have `vecv_(rain,road)=vecv_(rain,man)+vecv_(man,road)`………i ltbr. The two situations givenin the problem may be represented by the following ure. a. `vecv_(rain,road)` is same in magnitude and direction in bnogh the ures.
Taking horizontal components in equation i. for ure.
`v_(rain,road) sin alpha= 8km/h` ............ii.
Now consider ure. Draw a line `OA_|_ v_(rain, man)` as shown.
Taking components in equation i. along the line OA. `v_(rain, road) sin (30^0+alpha)=12 km/h cos 30^0`..........iii
From ii. and iii
`(sin(30^0+alpha))/(sin alpha)=(12xxsqrt13)/sqrt8xx2)`
`or, `(sin 3^0cosalpha+cos30^0 siN/Alpha)/(siN/Alpha)=(3sqrt(3)/4`
or `1/2 cot alpha + sqrt(3)/2=(3sqrt3)/4`
or, `cot alpha = sqrt3/2
or, ` alpha = cot^-1 sqrt3/2`
From ii, `v_(rain,road)=(8km/h)/(siN/Alpha)=4sqrt7 km/h`.
Promotional Banner

Similar Questions

Explore conceptually related problems

A man starts running along a straight road with uniform velocity observes that the rain is falling vertically downward. If he doubles his speed, he finds that the rain is coming at an angle theta to the vertical. The velocity of rain with respect to the ground is :

A man standing on a road has to hold his umbrella at 30^(@) with the vertical to keep the rain away. He throws the umbrella and starts running at 10km/hr. He finds that rain drop are hitting his head vertically. Find the speed of rain drops with respect to (a) road (b) the moving man.

A man when standstill observes the rain falling vertically and when he walks at 4 km//h he has to hold his umberella at an angle 53^(@) from the vertical. Find velocity of the raindrops.

A man moving with 5 ms^(-1) observes rain falling vertically at the rate of 10 ms^(-1) . Find speed of the rain with respect to ground.

Rain is falling vertically downwards with a velocity of 2m//s. A person is runing to the North with a velocity of 2sqrt(3) m/s. Find out the velocity and direction of rain as appeared to the person.

A person is walking to the east at 2 km/hr and the rain drops appear to him dropping vertically downwards at 2sqrt(3)km//hr . Find the actual velocity of rain.

Rain is falling vertically with a speed of 30 ms^(-1) . A woman rides a bicycle with a speed of 10 ms ^(-1) in the north to south direction . What is the direction in which she should hold her umbrella ?

A bus decreases its speed from 80 km h^(-1) to 60 km h^(-1) in 5s. Find the acceleration of the bus.

Rain is falling vertically with a speed of 20ms^(-1) ., A person is running in the rain with a velocity of 5 ms^(-1) and a wind is also blowing with a speed of 15 ms^(-1) (both from the west) The angle with the vertical at which the person should hold his umbrella so that he may not get drenched is: