- #1
Edwardo_Elric
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Homework Statement
Determined to test the law of gravity for himself,a student walks off a skyscraper 200 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.) What must be the magnitude of Superman's initial velocity so that he catches the student just before the ground is reached? (Assume superman's acceleration is that of any freely falling body. Superman leaves the roof with an initial speed Vo that he produces by pushing downward from the edge of the roof with his legs of steel).
b.) If the height of a skyscraper is less than some minimum value, even superman can't reach the student before he hits the ground. What is the minimum height?.
Homework Equations
y = Vot - 1/2(gt^2)
The Attempt at a Solution
t = student
t+5 = when superman arrives
Stuck with letter a
a.)
First i equate the two y positions:
y_{superman} = y_{student}
y_{student} = Vot - 1/2(gt^2)
y_{student} = - 1/2(gt^2)
y_{superman} = Vo(t + 5s) - 1/2(g(t+5s)^2)
y_{superman} = Vo(t+5s) - 1/2(9.8)(t^2+10t + 25)
= Vo(t+5s) - 1/2(9.8)t^2 - 5(9.8)t - 122.5t
Equate
y_{superman} = y_{student}
Vo(t+5s) - 1/2(9.8)t^2 - 5(9.8)t - 122.5t = - 1/2(9.8)(t^2)
cancel -1/2(9.8)t^2
Vo(t+5s) = 171.5t
Vo = 171.5t /(t+5s)