There is a crater of depth `R/100` on the surface of the moon (radius R). A projectile is fired vertically upwards from the crater with velocity, which is equal to theescape velocity v from the surface of the moon. Find the maximum height attained attained by the projectile.

A projectile is fired with velocity making an angle theta with the horizontal. Show that it follows a parabolic trajectory. Obtain an expression for the maximum height attained by it.

A body is thrown vertically upward with a velocity of 9.8 m//s^-1 Calculate the maximum height attained by the body. (g=9.8m//s^(2))

An object of mass m is raised from the surface of the earth to a heigt equal to the radius of the earth , that is, taken from a distance R to 2R from the centre of the earth. What is the gain in its potential energy?

A circle is the locus of a point in a plane such that its distance from a fixed point in the plane is constant. Anologously, a sphere is the locus of a point in space such that its distance from a fixed point in space in constant. The fixed point is called the centre and the constant distance is called the radius of the circle/sphere. In anology with the equation of the circle |z-c|=a , the equation of a sphere of radius a is |r-c|=a , where c is the position vector of the centre and r is the position vector of any point on the surface of the sphere. In Cartesian system, the equation of the sphere, with centre at (-g, -f, -h) is x^2+y^2+z^2+2gx+2fy+2hz+c=0 and its radius is sqrt(f^2+g^2+h^2-c) . Q. Equation of the sphere having centre at (3, 6, -4) and touching the plane rcdot(2hat(i)-2hat(j)-hat(k))=10 is (x-3)^2+(y-6)^2+(z+4)^2=k^2 , where k is equal to

A solid right circular cylinder has its radius equal to half of its height. Find the rate of change of its total surface area w.r.t. a change in the radius r.

Find the time required for a cylindrical tank of radius r and height H to empty through a round hole of area a at the bottom. The flow through the hole is according to the law v(t)=ksqrt(2gh(t)) , where v(t) and h(t) , are respectively, the velocity of flow through the hole and the height of the water level above the hole at time t , and g is the acceleration due to gravity.