2.8. EXERCISES 27
2.8 EXERCISES
2.1. e motion of ball is governed by the relation x D t
2
15t C 20; in which the distance
x is measured in m and t in s. Find (a) when the velocity is zero, and (b) the distance
traveled when t D 6 s.
2.2. e acceleration of an oscillating particle is defined by the equation a D kx: When
x D 0 and v D 8 m/s, find k.
2.3. In an experiment it was found that the acceleration of a particle is governed by the
relation a D g.1 kv
2
/: Knowing that the particle starts at t D 0; x D 0; and v D 0,
find an equation of velocity v for any distance x.
2.4. A driver of a car traveling at 60 km/h when he observes a traffic light 200 m ahead
turning red. e traffic light has been programmed to stay red for 20 s. If the driver
wants to pass the light without stopping just as it turns green again, determine the
required uniform deceleration of the car. It is assumed that the motion of the car is
rectilinear.
2.5. Slider block A travels to the right, in Figure 2.16, with a constant velocity of 10 m/s
and is connected by an inextensible cable to block B. It is assumed that no friction is
present between the block and the supporting horizontal surface, and between the cable
and pulley. Determine
A
B
C
D
x
A
y
B
y
C
y
D
+
+
Figure 2.16: Blocks traveling horizontally and vertically.
28 2. KINEMATICS OF PARTICLES
(a) the velocity of block B,
(b) the velocity of portion D of the cable, and
(c) the relative velocity of portion C of the cable with respect to portion D.
2.6. Slider Collar A travels to the left from rest with a constant acceleration, as shown in
Figure 2.17. Note that no friction is present between the collars and the horizontal
columns. e cable is inextensible. ere is no friction between the cable and pulleys.
Knowing that after 6 s the relative velocity of collar B respect to collar A is 10 m/s,
determine
(a) the accelerations of blocks
A
and
B
, and
(b) the velocity of block B after 5 s.
x
A
x
C
x
B
+
A
B
C
Figure 2.17: Collars traveling horizontally.
2.7. A projectile is fired with a velocity of 200 m/s at a target A located 650 m above the
gun G at a horizontal distance of 3,500 m, as shown in Figure 2.18. Disregarding air
resistance, find the firing angle ˛.
2.8. A fighter jet is flying horizontally, as shown in Figure 2.19, at an altitude of 3,000 m and
at constant speed of 900 km/h on a trajectory which passes directly over an anti-aircraft
gun which fires a shell with a muzzle velocity of 600 m/s and hits the jet. Knowing
that the firing angle of the gun is 58
ı
and disregarding air resistance, determine (a) the
velocity of the shell relative to the fighter jet at the time of impact and (b) the time it
takes from the gun to that at impact.
2.8. EXERCISES 29
3,500 m
200 m/s
650 m
A
G
α
Figure 2.18: Projectile firing.
900 km/h
3,000 m
58°
Figure 2.19: Impact of fighter jet and gun shell.
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