Answer to Question #142771 in Mechanics | Relativity for Shb

Question

A book of mass 250g is dropped vertically from a building 180m tall, where the wind provides and constant horizontal force of 5N on the book. What is the magnitude of the velocity of the book when it hits the ground?

Answer 1

Let x-axis be directed from the top of the building horizontally and y-axis be directed from the top of the building vertically downwards. Therefore, $\;v_x = \dfrac{F_w}{m}\cdot t, \;\;v_y = gt.$

$y = \dfrac{gt^2}{2}$ , so the time of the book's motion is $t = \sqrt{\dfrac{2H}{g}} = \sqrt{\dfrac{2\cdot180\,\mathrm{m}}{9.81\,\mathrm{m/s^2}}} \approx 6.1\,\mathrm{s}.$

$v_x(6.1\,\mathrm{s}) = \dfrac{5\,\mathrm{N}}{0.25\,\mathrm{kg}}\cdot6.1\,\mathrm{s} = 122\,\mathrm{m/s}$ , $\;\;v_y(6.1\,\mathrm{s}) = 9.81\,\mathrm{m/s^2}\cdot6.1\,\mathrm{s} = 59.8\,\mathrm{m/s}$ , so the total velocity will be $v = \sqrt{v_x^2+v_y^2} \approx 136\,\mathrm{m/s}.$

We can see that the horizontal velocity is very large. It is so because we assumed the horizontal force to be constant during all the motion of the book. If we assume the force to act only at the top of the building, the horizontal velocity will be significantly smaller