1. ## Superman problem

Determined to test the law of gravity for himself, a student walks off a skyscraper 180 m high, stopwatch in hand, and starts his free fall (zero initial velocity). Five seconds later, Superman arrives at the scene and dives off the roof to save the student.

a) Superman leaves the roof with an initial velocity that he produces by pushing himself downward from the edge of the roof with his legs of steel. He then falls with the same acceleration as any freely falling body. What must the value of the initial velocity be so that Superman catches the student just before they reach the ground?

b) On the same graph, sketch the positions of the student and of Superman as functions of time. Take Superman's initial speed to have the value calculated in part (a).

c) If the height of the skyscraper is less than some minimum value, even Superman can't reach the student before he hits the ground. What is this minimum height?

I have already tried to solve this, but I'm not sure about my answer. So I'm asking help right now from anyone who are willing. ---tnx

3. Originally Posted by ihmth
Determined to test the law of gravity for himself, a student walks off a skyscraper 180 m high, stopwatch in hand, and starts his free fall (zero initial velocity). Five seconds later, Superman arrives at the scene and dives off the roof to save the student.

a) Superman leaves the roof with an initial velocity that he produces by pushing himself downward from the edge of the roof with his legs of steel. He then falls with the same acceleration as any freely falling body. What must the value of the initial velocity be so that Superman catches the student just before they reach the ground?

b) On the same graph, sketch the positions of the student and of Superman as functions of time. Take Superman's initial speed to have the value calculated in part (a).

c) If the height of the skyscraper is less than some minimum value, even Superman can't reach the student before he hits the ground. What is this minimum height?

I have already tried to solve this, but I'm not sure about my answer. So I'm asking help right now from anyone who are willing. ---tnx
Here's what I got. Using $\displaystyle s = 4.9 \, t^2$ the student will fall the 180 m in $\displaystyle \sqrt{\frac{180}{4.9}} = 6.0609$ sec. Superman arrives after 5 sec. so he has 1.0609 sec to travel the 180 m

superman: $\displaystyle s = v_0 t + 4.9\, t^2$ so $\displaystyle 180 = v_0 * 1.0609 + 4.9 * 1.0609^2$ and solving for $\displaystyle v_0 = 164.47 m/s$
For (b) in the picture, red is the student and blue superman. I've started it at t = 5sec.
For part (c), if he reaches the ground with the 5 sec. so $\displaystyle s = 4.9*5^2 = 122.5 m$

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# a student decides to test law of gravity skyscraper

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