Question

The photo is 120 mm×90 mm. It is enlarged to 360 mm ×270 mm. The elephant's tail in the smaller photo is 15 mm long. How long is its tail in the larger photo? Show your calculations.

Answer 1

Scale about x-axis u = 360/120=3.

Scale about y-axis v = 270/90=3.

Let the tail be straight.

$S=\sqrt{X^2+Y^2}=\sqrt{(ux)^2+(vy)^2}=\\=\sqrt{9x^2+9y^2}=3\sqrt{x^2+y^2}=3s$

According to the conditions, s - length of the tail at small photo is equal 15, therefore S - lenght of the tail on the larger photo is equal 45.

Now let the tail be arbitrary.

$S=\int^{a}_{b}\sqrt{(\frac{dY}{dt})^2+(\frac{dX}{dt})^2}dt=\\ =\int^{a}_{b}\sqrt{(\frac{udy}{dt})^2+(\frac{vdx}{dt})^2}dt=\\ =3\int^{a}_{b}\sqrt{(\frac{dy}{dt})^2+(\frac{dx}{dt})^2}dt = 3s$

Length of the tail at the larger photo is equal 45