Answer to Question #304243 in Mechanics | Relativity for KING

Question

You are standing on the sci.com. building 46.0 m high above the ground. Your classmate, 1.8 m tall, is walking alongside the building at a constant speed of 1.20 m/s. If you wish to drop an egg onto his head,

a) where should he be when you release the egg? Assume that the egg is in free fall.

b) what will be the velocity of the egg when it hits his head?

Answer 1

The distance that egg should overcome is 46.0-1.8 = 44.2 meters.

Let us determine the time needed for the egg to change its height from 46.0 to 1.8 m. The initial velocity is 0, so the dependence will be

$1.8 = 46.0 - \dfrac{gt^2}{2}.$

So the time will be $t = \sqrt{\dfrac{2(46.0-1.8)}{g}} = 3$ s.

a) Therefore, our classmate should be at a distance of $3\,\mathrm{s}\cdot 1.20\,\mathrm{m/s} = 3.6\,\mathrm{m}$ when we release an egg.

b) The velocity after 3 seconds from the release will be $v = gt = 29.4\,\mathrm{m/s}.$