PROBLEM 11.91
The motion of a vibrating particle is defined by the position vector
(4sin ) (cos2 ) ,tt
rij where r is expressed in inches and t in
seconds. (a) Determine the velocity and acceleration when 1s.t
(b) Show that the path of the particle is parabolic.
PROBLEM 11.92
The motion of a particle is defined by the equations 10 5sin
x
tt
and 10 5cos ,yt
where x and y are
expresed in feet and t is expressed in seconds. Sketch the path of the particle for the time interval 02,t
and determine (a) the magnitudes of the smallest and largest velocities reached by the particle, (b) the
corresponding times, positions, and directions of the velocities.
PROBLEM 11.92 (Continued)
PROBLEM 11.92 (Continued)
PROBLEM 11.93
The damped motion of a vibrating particle is defined by the
position vector
/2
11
[1 1/ ( 1)] ( cos 2 ) ,
t
x
tye t
ri
j
where
t is expressed in seconds. For
1
30 mmx
and y
1
20 mm,
determine the position, the velocity, and the acceleration of the
particle when (a)
0,t
(b)
1.5 s.t
PROBLEM 11.93 (Continued)
Problem 11.94
A girl operates a radio-controlled model car in a vacant
parking lot. The girl’s position is at the origin of the xy
coordinate axes, and the surface of the parking lot lies in
the x–y plane. The motion of the car is defined by the
position vector
23
ˆˆ
(2 2 ) (6 )rtitj
where r and t
are expressed in meters and seconds, respectively.
Determine (a) the distance between the car and the girl
when t = 2 s, (b) the distance the car traveled in the interval
from t = 0 to t = 2 s, (c) the speed and direction of the car’s
velocity at t = 2 s, (d) the magnitude of the car’s
acceleration at t = 2 s.
PROBLEM 11.95
The three-dimensional motion of a particle is defined by the position vector r (Rt cos
nt)i ctj
(Rt sin
nt)k. Determine the magnitudes of the velocity and acceleration of the particle. (The space curve
described by the particle is a conic helix.)
PROBLEM 11.96
The three-dimensional motion of a particle is defined by the position
vector 2
(cos)( )(sin),
1
A
tt A Btt
t
ri
j
k where r and t are
expressed in feet and seconds, respectively. Show that the curve
described by the particle lies on the hyperboloid (y/A)2 (x/A)2
(z/B)2 1. For 3A
and 1,B
determine (a) the magnitudes of the
velocity and acceleration when 0,t
(b) the smallest nonzero value
of t for which the position vector and the velocity are perpendicular to
each other.
PROBLEM 11.96 (Continued)