Motion In A Plane

Resultant of two vectors and is of magnitude . If is reversed, then resultant is of magnitude . What is the value of ?

What is approximately the centripetal acceleration (in units of acceleration due to gravity on earth, ) of an air-craft flying at a speed of through a circular arc of radius ?

Particle moves along the line with constant velocity v of magnitude and directed parallel to the positive -axis (see figure). Particle starts at the origin with zero speed and constant accelerationa (of magnitude ) at the same instant that the particle A passes the y axis. The angle between a and the positive axis that would result in a collision between these two particles should have a value equal to

A shell fired from a gun at sea level rises to a maximum height of when fired at a ship away. The muzzle velocity should be

From a building two balls and are thrown such that is thrown upwards and downwards with the same speed (both vertically). If and are their respective velocities on reaching the ground then,

Three particles and are at rest at the vertices of an equilateral triangle of side . Each of the particles starts moving with constant speed is moving along along and along . The particles will meet each other at time given by

The expression of the trajectory of a projectile is given as , where and are respectively the vertical and horizontal displacements and and are constants. The time of flight of the projectile is