A projectile is launched at an angle `alpha` from a cliff of height H above the sea level. If it falls into the sea at a distance D from the base of the cliff, show that its maximum height above the sea level is
`[H+(D^(2) tan^(2) alpha)/(4(H+D tan alpha))]`

Explain why a person may bleed from the nose when at a great height above the sea level.

A fort is at the top of a hill of height h above the sea-level.Prove that the greatest horizontal distance from which a gun in the ship can hit the fort is 2sqrt(k(k-h)) where sqrt(2gk) is the muzzle velocity.

If the angle of elevation of a cloud from a point h metre above the lake is alpha and the angle of depression of its reflection in the lake is beta , prove that the height of the cloud above the lake is (h(tan beta+tan alpha))/(tan beta- tan alpha)

A tower subtends an angle alpha at a point on the same level as the foot of the tower and at the second point h metres above the first the angle of depression of the base of a tower is beta The height of the tower

The angle of elevation of a cloud from a height h above the level of water in a lake is alpha and the angle of depressionof its image in the lake is beta . Find the height of the cloud above the surface of the lake:

From the top of a light -house at a height 20 metres above sea -level,the angle of depression of a ship is 30^(@) .The distance of the ship from the foot of the light house is

A vertical tower Stands on a horizontal plane and is surmounted by a vertical flag staff of height h.At a point on the plane,the angles of Elevation of the bottom and the top of the flag staff are alpha and beta respectively Prove that the height of the tower is (h tan alpha)/(tan beta-tan alpha)

A vertical tower sands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane,the angles of elevation of the bottom and the top of the flagstaff are alpha and beta .Prove that the height of the tower (h tan alpha)/(tan beta-tan alpha)

A marble statue of height h_(1) metres is mounted on a pedestal.The angles of elevation of the top and bottom of the statue from a point h_(2) metres above the ground level are alpha and beta respectively.Show that the height of the pedestal is ((h_(1)-h_(2))tan beta+h_(2)tan alpha)/(tan alpha-tan beta)