Answer to Question #93538 in Mechanics | Relativity for E

Question

Lex Luthor drops Lois Lane from the roof of a building which has a height of 180m. Five seconds later, superman pushes himself off of this roof with an initial speed vo directed downwards towards Lois. After his feet leave the roof, superman accelerates downwards at the same rate as any other freely-faliling object.
How long after he leaves the roof does it take superman to catch up to Lois?
What must be the minimum value of vo so that superman can catch Lois just as they reach the ground?

Answer 1

Lois will fall for

$$T=\sqrt{2h/g}=6.06\text{ s}.$$

Thus, our superhero has only t=1.06 s to reach the ground. That is why his initial velocity downward should be calculated from the equation:

$$h=v_0t+gt^2/2,\\ v_0=159.42\text{ m/s}.$$