- #1

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**Determined to test the law of gravity for himself, a student walks off a skyscraper 180m high, stopwatch in hand, and starts his freefall (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 inital speed Vo, 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 his initial velocity be so that he reaches the student just before he hits the ground?

B) On the same graph sketch the position of the student and of Superman as functions of time. Take Superman's initial speed that was 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 groun What is this minimum height?

A) Superman leaves the roof with an inital speed Vo, 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 his initial velocity be so that he reaches the student just before he hits the ground?

B) On the same graph sketch the position of the student and of Superman as functions of time. Take Superman's initial speed that was 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 groun What is this minimum height?

My Solution:

a) First I found the time it would take for the student to fall 180 m. Using the equation x(t)=Xo+VoT+(1/2)at^2, I found this time to be 6.058s after I plugged in the numbers. It then says that Superman doesn't reach the scene until 5s after the student jumps, which would mean that he only has 1.058s left to save the student. So I then plugged those numbers into the same equation listed above and got an initial velocity of 31.0m/s downwards. It made sense to me at the time, but I am starting to doubt myself.

b) I was going to wait to draw that graph until I was sure of how to do a.

c) I'm not really sure how to do part c. I was thinking of making the two position functions equal to each other and solving for the height but I don't think that will work after all.

Thanks for any advice you can give.