(i) $$PQ$$ is a vertical tower. $$P$$ is the foot and $$Q$$ is the top of the tower. $$A, B, C$$ are three points in the horizontal plane through $$P$$. The angles of elevation of $$Q$$ from $$A$$, $$B$$, $$C$$ are equal, and each is equal to $$\theta $$. The sides of the triangle $$ABC$$ are $$a, b, c$$; and the area of the triangle $$ABC$$ is $$\Delta $$. Show that the height of the tower is $${{abc\tan \theta } \over {4\Delta }}$$.

(ii) $$AB$$ is vertical pole. The end $$A$$ is on the level ground. $$C$$ is the middle point of $$AB$$. $$P$$ is a point on the level ground. The portion $$CB$$ subtends an angle $$\beta $$ at $$P$$. If $$AP = n\,AB,$$ then show that tan$$\beta $$ $$ = {n \over {2{n^2} + 1}}$$

Give the MKS units for each of the following quantities.

(i) Young's modulus

(ii) Magnetic Induction

(iii) Power of a lens

A rocket moves forward by pushing the surrounding air backwards.

A ship of mass 3 $$ \times $$ 10⁷ kg initially at rest, is pulled by a force of 5 $$ \times $$ 10⁴ N through a distance of 3 m. Assuming that the resistance due to water is negligible, the speed of the ship is