A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60^o with ground level. But he finds the aeroplane right vertically above his position. If v is the speed of sound, speed of the plane is :

Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is -

The position co-ordinates of a particle moving in a 3-D coordinate system is given by
x = a cos$$\omega $$t
y = a sin$$\omega $$t and
z = a$$\omega $$t

The speed of the particle is :

A particle is moving with a velocity

$$\overrightarrow v \, = K(y\widehat i + x\widehat j),$$ where K is a constant.

The general equation for its path is :