Kinematics Questions: Solving for Superman's Velocity and Building Height

[Mehta29]

I understand the majority of introductory kinematics...except for these couple of questions...

Question #1

A student falls from a 300 M building and starts free fall, five seconds later, superman arrives and dives off the roof to save the student...

a) what must be superman's initial velocity to catch the student before he reaches the ground...

For this one, I figured for the student Vi=0, Vf=?, d=-300, a=-9.8, t = x and for superman Vi = x, Vf = ? d= -300, a = -9.8, t = x+5(or should it be -5?)

For time I get 7.8 seconds by -300= ViT - 1/2(-9.8)t^2 but if I plug that into -300 = Vi(12.8) - 1/2(-9.8)(12.8)^2 i get 86 m/s which seems very unreasonable...I think I'm doing something wrong mathematically, help would be appreciated...


b)What is the minimum height that the building can be for superman to be able to save the student...How I would approach this problem...I'm just drawing blanks, again any help would be greatly appreciated...What variables would I set equal to each other?

#2

A student is trying to catch a bus, which is at rest 80 m away. She runs at a constant velocity of 8 m/s, and the bus accelerates at a rate of .2 m/s^2

a) What min speed would she have to go to catch up with the bus?

I'm thinking of graphically solving this but what exactly would I graph, I know the distances of both would be set equal, and that the person has a=0, while the bus has a=.2, but how would i manage to derive an equation out of all of this...

b) How long and how far will she have to run?
I guess this part is pretty much dependent on a) which I just need the velocity for and I can figure everything out. But I'm really stuck on what to do for part a)

Thanks again for your guys help...you guys have been great for a couple of my friends who've already taken AP Physics...too bad they're too busy with their college lives...but I hope I've been clear enough on what I need help with...

Thanks...

 

[Andrew Mason]

I think you are supposed to assume that superman starts with an initial non-zero velocity downward and accelerates only due to gravity. Do a graph of velocity vs time. The area under the graph is the distance.
Since superman starts late, he has some distance to make up (the area under the student's graph to the left of the time when superman starts). The area between superman's graph and that of the falling student is the distance that he makes up on the student. That area has to be equal to or greater than the initial distance he has to make up.

AM

 

[andrevdh]

Q1
a) The initial time you calculated is for the student to fall the total distance of 300 meters. So SS has (7.8 - 5) seconds of time left to save the student.

b) I think this would be the distance that the student dropped through for the first 5 seconds. So SS has just a fraction of a second time to save him/her. Using his super powers he will then need to start with a very large intial speed.

Q2
a) Maybe plot the distances covered by the student and the bus. Take the reference point for the distance measurements as the starting point of the student. So when time is zero the bus starts at a distance of 80 meters.