HARD
JEE Main
IMPORTANT
Earn 100

An aeroplane has to go from a point A to another point B500 km away due 30° east of north. The wind is blowing due north at a speed of 20 m s-1. The air-speed of the plane is 150 m s-1.

(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.

Important Questions on Rest and Motion : Kinematics

HARD
JEE Main
IMPORTANT
Two friends A and B are standing at a distance x apart in an open field and the wind is blowing from A to B. A beats a drum and B hears the sound at time t1 after he sees the event. A and B interchange their positions and the experiment is repeated. This time, B hears the drum at time t2 after he sees the event. Calculate the velocity of sound in still air v and the velocity of wind u. Neglect the time that light takes in travelling between the friends.
HARD
JEE Main
IMPORTANT

Previous Problem: Two friends A and B are standing at a distance x apart in an open field and the wind is blowing from A to B. A beats a drum and B hears the sound at time t1 after he sees the event. A and B interchange their positions and the experiment is repeated. This time, B hears the drum at time t2 after he sees the event. Calculate the velocity of sound in still air v and the velocity of wind u. Neglect the time that light takes in travelling between the friends.

Consider A and B in the previous problem. Change their positions in such a way that the line joining them becomes perpendicular to the direction of the wind while maintaining the separation x. What will be the time lag B finds between seeing and hearing the drum beating by A?

MEDIUM
JEE Main
IMPORTANT

Six particles, situated on the corners of a regular hexagon of side a, move at a constant speed v. Each particle maintains a direction towards the particle at the next corner. Calculate the time the particles will take to meet each other.