A particle is projected from origin with speed `u`. Find the minimum value of `u` if the particle passes through a poiny `P (a, sqrt(3)a)`.

Assume that there is a smooth tunnel of depth (R )/(2) along a diameter of earth. A particle is projected from the bottom of tunnel with speed u. Find the minimum value of u so that the particle is able to escape the gravitational field of earth. M and R represents mass and radius of earth

A particle is projected vertically upwards in vacuum with a speed u .

A particle is projected vertically upwards in vacuum with a speed u .

A particle is projected from the origin in such a way that it passes through a given point P (a, b} What is the minimum requrired speed to do so?

A particle is projected at an angle theta with an initial speed u .

A particle is projected at an angle theta from ground with speed u (g = 10 m/ s^2 )

A particle is projected on an inclined plane with a speed u as shown in (Fig. 5.61). Find the range of the particle on the inclined plane. .

A particle is projected on an inclined plane with a speed u as shown in (Fig. 5.61). Find the range of the particle on the inclined plane. .

In a region, potential energy varies with X as U(x)=30-(x-5)^(2) Joule, where x is in meters. A particle of mass 0.5 kg is projected from x=11 m towards origin with a velocity 'u' . u is the minimum velocity, so that the particle can reach the origin. (x=0). find the value of u/2 in meter/second. (Take sqrt(44)=6.5 )

In a region, potential energy varies with X as U(x)=30-(x-5)^(2) Joule, where x is in meters. A particle of mass 0.5 kg is projected from x=11 m towards origin with a velocity 'u' . u is the minimum velocity, so that the particle can reach the origin. (x=0). find the value of u/2 in meter/second. (Take sqrt(44)=6.5 )