An arch way is in the shape of a semi-ellipse, the road level being the major axis. If the breadth of the arch way is 30 feet and a man 6 feet tall just touches the top when 2 feet from the side, find the greatest height of the arch.

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

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

A person standing on the bank of a river observers that the angle subtends by a tree on the opposite bank is 60^(@) . When he retires 40 feet from the bank, he finds the angle to be 30^(@) . Find the height of the tree and the breadth of the river.

A man sitting at a height of 20m on a tall tree on a small island in the middle of a river observes two poles directly opposite to each other on the two banks of the river and in line with the foot of tree. If the angles of depression of the feet of the poles from a point at which the man is sitting on the tree on either side of the river are 60^0a n d30^0 respectively. Find the width of the river.

A thin equiconvex glass lens (mu_(g)=1.5) is beign placed on the top of a vessel of height h=20cm as shown figure. A luminous point source is beign placed at the bottom of vessel on the principal axis of the lens. When the air is on both the side of the lens the image of luminous source is formed at a distance of 20cm from the lens out side the vessel. When the air inside the vessel is being replaced by a liquid of refractive index mu_(l) the image of the same source is being formed at a distance 30cm from the lens outside the vessel. Find the mu_(l) .

A man is moving away from a 40-m high tower at a speed of 2 m/s. Find the rate at which the angle of elevation of the top of the tower is changing when he is at a distance of 30 metres from the foot of the tower. Assume that the eye level of the man is 1.6 m from the ground.