On a certain day, rain was falling vertically with a speed of `35ms^(-1)` . A wind started blowing after sometime with a speed of `12ms^(-1)` in east to west direction . In which direction should boy waiting at a bus stop hold his umbrella ?

A projectile is thrown with a speed of 98 ms^(-1) in a direction 30^(@) above the horizontal . Find the time of flight , range and height to which it rises .

A train standing in a station-yard, blows a whistle of frequency 400Hz in still air. The wind starts blowing in the direction from the yard to the station with a speed of 10 ms^(-1) . What are the frequency wavelength and speed of sound for an observer standing on the station.s platform? Is the situation exactly identical the case when the air is still and the observer runs towards the yard at a speed of 10 ms^(-1) ? The speed of sound in still air can be taken as 340 ms^(-1)

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. Find the speed and direction of the rain with respedt to the road.

An aeroplane has to go from a point A to another point B, 500 km away due 30^@ east of north. Wind is blowing due north at a speed of 20 m//s. The air-speed of the plane is 150 m//s. (a) Find the direction in which the pilot should head the plane to reach the point B. (b) Find the time taken by the plane to go from A to B.

A proton is projected with a speed of 3X10^6 ms ^(-1) horizontally from est to west. A uniform magnetic field vec B of strength 2.0X10^(-3) T exists in the vertically upward direction(a) find the force on the proton just after it is projected. (b) what is the acceleration produced?

A lighter particle moving with a speed of 10 ms^(-1) collides with an object of double its mass moving in the same direction with half its speed. Assume that the collision is a one dimensional clastic collision. What will be the speed of both particles after the collision?

A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0ms^(-1) , at right angles to the horizontal component of the earth's magnetic field, 0.30xx10^(-4)Wbm^(-2) . a. What is the instantaneous value of the emf induced in the wire? b. What is the direction of the emf? c. Which end of the wire is at the higher electrical potential?

A wave travels along the positive x-direction with a speed of 20 ms^-1 . The amplitude of the wave is 0.20 cm and the wavelength 2.0 cm. (a) Write a suitable wave equation which describes this wave. (b) What is the displacement and velocity of the particle at x = 2.0 cm at time t = 0 according to the wave equation written ?

A 10 g bullet having a charge of 4.00 muC is fired at a speed of 270 ms^(-1) in a horizontal direction. A vertical magnetic field of 500 muT exists in the space. Find the deflection of the bullet due to the magnetic field as it travels through 100m. make appropriate approximations.