An arch is in the form of a semi - ellipse. If is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.

An arch is in the from of a semi - ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.

An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola ?

IF the distribution of weight is uniform, then the rope of the suspended bridge takes the form of parabola.The height of the supporting towers is 20m, the distance between these towers is 150m and the height of the lowest point of the rope from the road is 3m. Find the equation of the parabolic shape of the rope considering the floor of the parabolic shape of the rope considering the floor of the bridge as X-axis and the axis of the parabola as Y-axis. Find the height of that tower which supports the rope and is at a distance of 30 m from the centre of the road.

A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.

A iron pillar consists of a cylindrical portion of 2.8 m height and 20 cm in diameter and a cone of 42 cm height sumounting it. Find the weight of the pillar if 1 cm^3 of iron weights 7.5 g.

A tent is in the form of a cylinder of diameter 4.2 m and height 8 m surmounted by a conc of equal base and heitght 6m, find the volume of air in the tent.

A tent is in the slape of a cylinder surmounted by a conical top If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively and the slant height of the top is 2.8 m. find the area of the canvas used for making the tent. Find the cost of the canvas of the tent at the rate of 500 per m^2 .

Two poles of equal heights are standing opposite each other on either side of the road, which is 80m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60^(@) and 30^(@) , respectively. Find the height of the poles and the distances of the point from the poles.

Find the potential energy of the gravitational interation of a point mass of mass m and a thin uniform rod of mass M and length l, if they are located along a straight line such that the point mass is at a distance 'a' from one end. Also find the force of their interaction.

A particle is projected with a velocity 10 m/s at an angle 37^(@) to the horizontal. Find the location at which the particle is at a height 1 m from point of projection.