Question

Two towers, A and B standing vertically on a horizontal ground appear in a vertical aerial photograph as shown in the figure.


The length of the image of the tower A on the photograph is 1.5 cm and of the tower B is 2.0 cm. The distance of the top of the tower A (as shown in the arrowhead) is 4.0 cm and the distance of the top of the tower B is 6.0 cm as measured from the principal point p of the photograph. If the height of the tower B is 80 m the height (in meters) of the tower A is _____

• A. 90

Answer 1

The correct option is A 90


For Tower B,

Radial distance of top of tower = r = 6cm

Length of image = d = 2 cm

$\text{Height of tower = 80 m =}{h}_2$

$\therefore \text{Flying height above datum}=H-h_1$

$\because d=\frac{r{h}_2}{H-h_1}$

$\Rightarrow H-h_1=\frac{r{h}_2}{d}=\frac{6\times 80}{2}=240m$

For Tower A,

$\because$ Both on same plane

$d=\frac{r{h}_2}{H-h_1}$

r = 4 cm

d = 1.5 cm

$H-h_1=240m$

$h_2=\frac{d\times (H-h_1)}{r}=\frac{1.5\times 240}{4}$

$h_2=90m$