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.
|
SOLUTION :
Using a coordinate system with x=0 at the door of the stopped
bus.
Initial position of man at t=0 is xo=-b
speed of man = v = c
Motion of man is uniform (without acceleration) with constant
velocity 'c' in positive direction
A.
The position of the man as a function of time is given by x = xo + vt
x_man_(t)= - b+ c t
B.
Bus starts from origin,
Initial position of the bus is: xo=zero
Bus starts from rest, initial velocity of bus = vo = 0
Acceleration of bus= a =a
For motion with constant acceleration, the equation of motion is :
x = xo+vot +(1/2)at^2
The motion of bus is with constant acceleration, the equation of
motion of bus is :
x_bus_(t) = zero +zero +(1/2)at^2
x_bus_(t) = (1/2)at^2
____________________________
C . Assume he catches it at time t_catch. The possible answers for
the condition necessary for the man to catch the bus are
x_man_(t_catch_) = x_bus_(t_catc...
Get Answers For Free
Most questions answered within 1 hours.