Question

You are on the roof of a building, 46.0 m above the ground. Your friend, who is 1.80 m tall, is standing next to the building. What speed would an egg dropped from rest be traveling when it hit your friend on the top of his head?

Answer 1

Answer:

29.448 $ms^{-1}$

Explanation:

first determine the distance from the top of the roof to the friends head.

Since he is 1.80 min height ,

distance =  46.0-1.80

              = 44.2 m

egg is dropped from rest means that its starting velocity is zero. It has to travel 44.2 m subjected to the gravitational acceleration

Applying  Motion equation

$v^{2}=u^{2}+2as$

where v= end velocity (speed)

           u=Starting velocity

           a= acceleration

           s= Distance

(Let gravitational acceleration assumed as $9.81 ms^{-2}$

$v^{2} =0^{2} +2*9.81*44.2\\v^{2} =867.204\\v=\sqrt{867.204} \\v=29.448 ms^{-1}$

Answer 2

Answer:

The speed of egg is 14.73 m/s

Explanation:

Given the height of building (H) = 46 m

The height of friend (h) = 1.8 m

Distance for the egg to travel (s) = H – h = 46 – 1.8 = 44.2 m

Applying second equation of motion,

$s=u t+\frac{1}{2} g t^{2}$

u = 0 (as the egg is starting from the rest)

g = 9.81 $m/s^2$(as the object is falling)

Substituting the values,

44.2=0+$\frac{1}{2} \times9.81 \times t^{2}$

$t^{2}=\frac{44.2 * 2}{9.81}$

$t^2$ = 9

t = 3 sec

Calculating speed,

Speed =   $\frac{\text { Distance }}{\text { time }}$

Speed = $\frac{44.2}{3}=14.73 \mathrm{m} / \mathrm{s}$

Therefore, the speed of egg is 14.73 m/s