In: Physics
A man is running at speed c (much less than the speed
of light) to catch...
A man is running at speed c (much less than the speed
of light) to catch a bus already at a stop. At t=0, when
he is a distance b from the door to the bus, the bus
starts moving with the positive acceleration a.
Use a coordinate system with x=0 at the door of the
stopped bus.
a)
What is xman(t), the position of the man as a
function of time?
Answer symbolically in terms of the variables b,
c, and t.
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xman(t) =
b)
What is xbus(t), the position of the bus as a
function of time?
Answer symbolically in terms of a and t.
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xbus =
c)
What condition is necessary for the man to catch the bus? Assume
he catches it at time tcatch.
What condition is necessary for the man to catch the bus? Assume
he catches it at time .
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xman(tcatch)>xbus(tcatch) |
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xman(tcatch)=xbus(tcatch) |
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xman(tcatch)<xbus(tcatch) |
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c=a?tcatch
d)
Inserting the formulas you found for xman(t)
and xbus(t) into the condition
xman(tcatch)=xbus(tcatch), you
obtain the following:
?b+ctcatch=12at2catch,
or
12at2catch?ctcatch+b=0.
Intuitively, the man will not catch the bus unless he is running
fast enough. In mathematical terms, there is a constraint on the
man's speed c so that the equation above gives a solution
for tcatch that is a real positive number.
Find cmin, the minimum value of c for which
the man will catch the bus.
Express the minimum value for the man's speed in terms of
a and b.
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