Show that a given gun will shoot three times as high when elevated at an angle of `60^@` as when fired at angle of `30^@` but will carry the same distance on a horizontal plane.

Shib is flying kite having the length of thread 250 metres, when the thread makes an angle 60^(@) with the horizontal line and when the thread makes an angle of 45^(@) with the horizontal line. Calculate in each case what is the height of kite from the ground. Also find in which of the two cases will the kite be at a greater height from the other.

The shadow of a flagstaff is three times as long as the shadow of the flagstaff when the sun days meet the ground at an angle of 60^@ . Find the angle between the sun rays and the ground at the time of longer shadow?

From the foot of a 60m high tower the angle of elevation of a minar is 60^@ and from the top, it is 30^@ . Find the height of the minar.

A man standing on the deck of a ship, which is 10m above the water level, observes the angle of elevation of the top of a hill as 60^@ and the angle of depression of the base of the hill as 30^@ . Calculate the distance of the hill from the ship and the height of the hill.

A square coils of side 10 cm consists of 20 turns and carries a current of 12A. The coil is suspended vertically and the normal to the plane of the coil makes an angle of 30^(@) with the direction of a uniform horizontal magnetic field of magnitude 0.80T . What is the magnitude to torque experienced by the coil ?

What is a projectile .Show that the path following by a projectile is a parabolic when it is projected at an angle theta with the horizontal. Obtain an expression for Horizontal range.

A stone ,thrown with the same initial speed ,rises 20 m higher when the angle of projection changes from 30^@ to 60^@ . What was the initial speed and the increases in time spent by the stone in air in the second case ?

A gun fires at an angle 30^@ with the horizontal and hits a target at a distance of 3 km . Can another target at a distance of 5km be hit by changing the angle of projection but keeping the velocity of projection unchanged ?