An arch is in the shape of a parabola whose axis is vertically downward and measures 80 meters across the bottom on the ground. Its highest point is 24 meters. Then the measure of the horizontal beam across the section at a height of 18 meters is

In a model, it is shown that an arc of a bridge is semi elliptical with major axis horizontal. If the length of the base is 9m and the highest part of the bridge is 3m from the horizontal, then the height of the arch, 2m from the centre of the base is (in meters)

From the top of a tower,the angle of depression of a point P on the ground is 30^(@) . If the distance of the point P from the tower be 24 meters then height of the tower is

A vertical pole fixed to the horizontal ground is divided in the ratio 3 : 7 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground 18 m away from the base of the pole, then the height of the pole (in meters) is :

The distance of a particle moving on a circle of radius 12 m measured from a fixed point on the circle and measured along the circle is given by s=2t^(3) (in meters). The ratio of its tangential to centripetal acceleration at t = 2s is

The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be alpha . After moving a distance 2 meters from P towards the foot of the tower, the angle of elevation changes to beta . Then the height (in meters) of the tower is :

Some portion of a 20 meters long tree is broken by the wind and its top struck the ground at an angle of 30 ^@ .Find the height of the point where the tree is broken.

A small sphere rolls down without slipping from the top of a track in a vertical plane. The track has an elevated section and a horizontal part. The horizontall part is 1.0 meter above the ground level and the top of the track is 2.4 meter above the ground. Find the distance on the ground with respect to a point B ( which is vetically below the end A of the track as shown in fig.) where the sphere lands. . (A) 1 m (B) 2 m ( C) 3 m (D) 4 m .

A ball is thrown horizontally from the top of a lower of unkown height .Ball strikes a vertical wall whose plane is normal to the plane of month of ball Collison is elastic and ball falls on ground exactly at the midpoints between the lower and the wall ball strikes the grouind at an angle of the 30^(@) with horizontal .Find the hieght of the tower (in meter)

Taking horizontal ground as xz - plane and y-axis vertically upwards. A particle is projected from the horizontal ground from a point whose position vector is hati_hatk meter with initial velocity from the origin when it hits ground is given by (1)/(5)[11hati+n hatk] , find n . (Take g = 10 m//s^(2) in negative y - direction)