Question

You are on the roof of the physics building, 46.0 above the ground . Your physics professor, who is 1.80 tall, is walking alongside the building at a constant speed of 1.20m/s. If you wish to drop an egg on your professor's head, how far from the building should the professor be when you release the egg?

Answer 1

Answer:

3.6m

Explanation:

if you are at a building that is 46m above the ground, and the professor is 1.80m, the egg must fall:

46m - 1.80m = 44.2m

the egg must fall for 44.2m to land on the head of the professor.

Now, how many time this takes?

we have to use the following free fall equation:

$h=v_{0}t+\frac{1}{2}gt^2$

where $h$ is the height, $v_{0}$ is the initial velocity, in this case $v_{0}=0$. $g$ is the acceleration of gravity: $g=9.81m/s$ and $t$ is time, thus:

$h=\frac{1}{2}gt^2$

clearing for time:

$2h=gt^2\\\frac{2h}{g}=t^2\\\sqrt{\frac{2h}{g}} =t$

we know that the egg has to fall for 44.2m, so $h=44.2$, and $g=9.81m/s$, so we the time is:

$t=\sqrt{\frac{2(44.2m)}{9.8m/s^2} }=\sqrt{\frac{88.4m}{9.81m/s^2} } =\sqrt{9.011s^2}= 3.002s$

Finally, if the professor has a speed of $v=1.2m/s$, it has to be at a distance:

$d=vt$

and t=3.002s:

$d=(1.2m/s)(3.002s)=3.6m$

so the answer is the professor has to be 3.6m far from the building when you release the egg