Catch/Overtake Problems Video Lessons

Concept

# Problem: 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.b) What is xbus(t), the position of the bus as a function of time? Answer symbolically in terms of a and t.c) What condition is necessary for the man to catch the bus? Assume he catches it at time tcatch.a. xman(tcatch) &gt; xbus(tcatch)b. xman(tcatch) = xbus(tcatch)c. xman(tcatch) &lt; xbus(tcatch)

###### FREE Expert Solution

Uniform accelerated motion (UAM) equations, a.k.a. "kinematics equations":

(a)

For constant speed:

Δx = ct

xfinal - xinitial = ct

xfinal = xinitial + ct

xfinal = xman

Assuming the bus is moving in a positive direction, xinitial = -b

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###### Problem Details

A man is running at speed c (much less than the speed of light) to catch a bus already at a stop. At = 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 = 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.

b) What is xbus(t), the position of the bus as a function of time? Answer symbolically in terms of a and t.

c) What condition is necessary for the man to catch the bus? Assume he catches it at time tcatch.

a. xman(tcatch) > xbus(tcatch)

b. xman(tcatch) = xbus(tcatch)

c. xman(tcatch) < xbus(tcatch)