Question

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.

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.

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 .

xman(tcatch)>xbus(tcatch)

xman(tcatch)=xbus(tcatch)

xman(tcatch)<xbus(tcatch)

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.

cmin =

Expert Solution

genius_generous answered 6 months ago

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