Motion in a Pla...

A shell is fired from a canon with a velocity v at angle θ with horizontal. At the highest point, it explodes into two pieces of equal mass. One of the pieces retraces its path to the canon. The speed of the other piece just after explosion is

Two stones are projected with thesame velocity, in magnitude butmaking different angles with thehorizontal. Their ranges are equal. If the angle of projection of one is π/3 and its maximum height is y₁, thenthe maximum height of the other willbe

A person aims a gun at a bird from a point, at a horizontal distance of 100m. If the gun can impact a speed of 500 ms^–1 to the bullet at what height above the bird must he aim his gun in order to hit it? (g = 10 ms^–2)

A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at t = 0. At this instant of time, the horizontal component of its velocity is v. A bead Q of the same mass as P is ejected from A at t = 0 along the horizontal string horizontal string AB (see fig.) with the speed v. Friction between the bead and the string may be neglected. Let t_P and t_Q be the respective times taken by P and Q to reach the point B. Then

A particle rests on the top of a hemisphere of radius R. Find the smallest horizontal velocity that must be imparted to the particle if it is to leave the hemisphere without sliding down it.

A particle performing uniform circular motion has

A Car is moving with speed 30 m/s on a circular path of radius 500 m. Its speed is increasing at the rate of 2 m/s². What is the acceleration of the car