Motion in a Pla...

A cart is moving horizontally along a straight line with constant speed 30 ms ^-1. A projectile is to be fired from the moving cart in such a way that it will return to the cart after the cart has moved 80 m. At what speed (relative to the cart) must the projectile be fired? (take, g =10 ms ^-2)

For a particle in uniform circular motion, the acceleration a at a point P(R, θ) on the circle of radius R is (here θ is measured from the X–axis)

A particle is moving in a circle of radius R in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at t = 0 is v₀, the time taken to complete the first revolution is

A particle of mass m is projected from the ground with an initial speed u₀ at an angle with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u₀. The angle that the composite system makes with the horizontal immediately after the collision is

The path of projectile is given by the equation y = ax - bx² , where a and b are constants and x and y are respectively horizontal and vertical distances of projectile from the point of projection. The maximum height attained by the projectile and the angle of projection are respectively.

A small particle of mass m is projected at an angle θ with the X–axis with an initial velocity v_o in the X–Y plane as shown in the figure. At a time

A particle is projected with certain velocity at two different angles of projections with respect to horizontal plane so as to have same range R on a horizontal plane. If t₁ and t₂ are the time taken for the two paths, which one of the following relations is correct?