The angle of elevation of jet fighter from a point $P$ on the ground is ${60}^{\mathrm{o}}$. After $5$ s of flight, The angle of elevation changes to ${45}^{\mathrm{o}}$. If the jet is flying at a height of $3000$ m, then the speed of the jet (In m/s) is

A telegraph post gets broken at a point against a storm and its top touches the ground at a distance $20$ m from the base of the post making an angle ${30}^{\mathrm{o}}$ with the ground. What is the height of the post?

A portion of a $30$ m long tree is broken by tornado and the top struck up the ground making an angle ${30}^{\mathrm{o}}$ with ground level. The height of the point where the tree is broken, is equal to:

The angle of elevation of the top of a tower from the bottom of a building is twice than that from its top. What is the height of the building if the height of the tower is $75$ metre and the angle of the top of the tower from the bottom of the building is ${60}^{\mathrm{o}}$?