Home
Class 12
PHYSICS
A man standing on a road has to hold his...

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.

Text Solution

Verified by Experts

The correct Answer is:
`2/(sqrt(2)+1)`
For stone : `2h=((u sin theta)^(2))/(2g)` & `h=(u sin theta)t-1/2 g t^(2)`
`rArr t=(sqrt(40h)+-sqrt(20h))/(10)rArr Deltat=sqrt(0.8h)=2/10 sqrt(20 h)`

Horizontal displacement : `vt_(2)=u cos theta Deltat`
`rArr (v(sqrt(2)+1)sqrt(20h))/10=u cos thetaxx(2sqrt(20h))/10`
`rArr v/(u cos theta)=(2)/(sqrt(2)+1)`
Promotional Banner

Topper's Solved these Questions

  • MOTION IN A PALNE

    ALLEN |Exercise Exercise-05 [A]|11 Videos

  • MOTION IN A PALNE

    ALLEN |Exercise Exercise-05[B]|5 Videos

  • MOTION IN A PALNE

    ALLEN |Exercise EXERCISE-04[A]|35 Videos

  • KINEMATICS-2D

    ALLEN |Exercise Exercise (O-2)|47 Videos

  • NEWTON'S LAWS OF MOTION & FRICTION

    ALLEN |Exercise EXERCISE (JA)|4 Videos

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 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.

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.

A man is walking on a road with a velocity 3kmhr. Suddenly rain starts falling. The velocity of rain is 10km/hr in vertically downward direction. the relative velocity of rain with respect to man is :-

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 is moving due east with a speed 1 km/hr and rain is falling vertically with a speed sqrt(3) km/hr. At what angle from vertical the man has to hold his umbrella to keep the rain away. Also find the speed of rain drops w.r.t. man.

A man walking briskly in rain with speed v must slant his umbrella forward making an angle theta with the vertical. A student derives the following relation between theta and v: tan theta = v and checks that the relation has a correct limit : as vtoo, thetato0 , as expected , (we are assuming there is no strong wind and that the rain falls vertically for a stationary man.) Do you think this relation can be correct ? If you, guess the correct relation.

By the term velocity of rain, we mean velocity with which raindrops fall relative to the ground. In absence of wind, raindrops fall vertically and in presence of wind raindrops fall obliqucly. Moreover raindrops acquire a constant terminal velocity due air resistance very quickly as they fall toward the carth. A moving man relative to himself observes an altered velocity of raindrops. Which is known as velocity of rain relative to the man. It is given by the following equation. vec(v)_(rm)=vec(v)_(r)-vec(v)_(m) A standstill man relative to himself observes rain falling with velocity, which is equal to velocity of the raindrops relative to the ground. To protect himself a man should his umbrella against velocity of raindrops relative to himself as shown in the following figure. When you are standstill in rain, you have to hold umbrella vertically to protect yourself. (a) When you walk with velocity 90 cm/s, you have to hold your umbrella at 53^(@) above the horizontal. What is velocity of the raindrops relative to the ground and relative to you ? (b) If you walk with speed 160 cm/s, how should you hold your umbrella ?

A man drives his car uniformly at 30 km/h for three hour After it he covered next 90 km distance with uniform speed of 45 km/hr. Find the average speed of car.

A ball was thrown by a boy a at angle 60^(@) with horizontal at height 1 m from ground. Boy B is running in the plane of motion of ball and catches the ball at height 1 m from ground. He finds the ball falling vertically. If the boy is running at a speed 20 km/hr. Then the velocity of projection of ball is-