Fundamentals of College Physics Chapter 03

[ Pobierz całość w formacie PDF ]

the car be moving when it overtakes the ball rise? initial velocity of 35.0 m/s at an
the truck? *59. A helicopter, at an altitude angle of 45.00 above the horizontal.
*52. A boat passes a buoy while of 300 m, is rising vertically at 20.0 Will the ball clear a 3.00 m fence
moving to the right at a velocity of m/s when a wheel falls off. How 92.0 m from home plate for a home
8.00 m/s. The boat has a constant high will the wheel go with respect run? If so, by how much will it clear
acceleration to the left, and 10.0 s to the ground? How long will it take the fence?
later the boat is found to be moving for the wheel to hit the ground *66. A ball is thrown from a
at a velocity of -3.00 m/s. Find below? At what velocity will the bridge 100 m high at an initial
(a) the acceleration of the boat, wheel hit the ground? velocity of 30.0 m/s at an angle of
(b) the distance from the buoy when 50.00 above the horizontal. Find
the boat reversed direction, (c) the (a) how high the ball goes, (b) the
time for the boat to return to the total time the ball is in the air,
buoy, and (d) the velocity of the (c) the maximum horizontal
boat when it returns to the buoy. distance that the ball travels, and
*53. Two trains are initially at (d) the velocity of the ball as it
rest on parallel tracks with train 1 strikes the ground.
50.0 m ahead of train 2. Both trains 67. A ball is thrown at an angle
accelerate simultaneously, train 1
of 35.50 below the horizontal at a
at the rate of 2.00 m/s2 and train 2
speed of 22.5 m/s from a building
at the rate of 2.50 m/s2. How long
20.0 m high. (a) How long will it
will it take train 2 to overtake train
take for the ball to hit the ground
1? How far will train 2 travel before
below? (b) How far from the
it overtakes train 1?
building will the ball land?
Diagram for problem 59.
*54. Repeat problem 53 but
*68. Using the kinematic
with train 1 initially moving at 5.00
equations for the x- and y-
*60. A ball is dropped from the
m/s and train 2 initially moving at
components of the displacement,
roof of a building 40.0 m high.
7.00 m/s.
find the equation of the trajectory
Simultaneously, another ball is
*55. A policewoman driving at
for two-dimensional projectile
thrown upward from the ground
80.0 km/hr observes a car 50.0 m
motion. Compare this equation with
and collides with the first ball at
ahead of her speeding at 120 km/hr.
the equation for a parabola
half the distance to the roof. What
If the county line is 400 m away
expressed in its standard form.
was the initial velocity of the ball
from the police car, what must the
*69. Using the kinematic
that was thrown upward?
acceleration of the police car be in
equations, prove that if two balls
*61. A ball is dropped from the
order to catch the speeder before he
are released simultaneously from a
top of a 40.0-m high building. At
leaves the county?
table, one with zero velocity and the
what initial velocity must a second
*56. Two trains are approaching
other with a horizontal velocity v ,
0x
ball be thrown from the top of the
each other along a straight and
they will both reach the ground at
building 2.00 s later, such that both
level track. The first train is
the same time.
balls arrive at the ground at the
heading south at 125 km/hr, while
same time?
the second train is heading north at
Interactive Tutorials
*62. Show that the range of a
80.0 km/hr. When they are 2.00 km
70. A train accelerates from an
projectile is the same for either a
apart, they see each other and start
initial velocity of 20.0 m/s to a final
projection angle of 45.00 +� or an
to decelerate. Train 1 decelerates at
velocity of 35.0 m/s in 11.8 s. Find
angle of 45.00 -�.
2.00 m/s2, while train 2 decelerates
its acceleration and the distance the
63. A projectile hits a target
at 1.50 m/s2. Will the trains be able
train travels in this time.
1.50 km away 10.5 s after it was
to stop or will there be a collision?
Chapter 3 Kinematics - The Study of Motion 3-41
71. A ball is dropped from a t. (f) Plot a picture of the motion as
"x
v = lim
building 50.0 m high. How long will a function of time.
"t�!0
"t
it take the ball to hit the ground 75. Generalized two-
below and with what final velocity? dimensional projectile motion. A
For an acceleration with a
Plot the displacement and the projectile is fired from a height y
displacement given by x = 0.5 at2,
velocity of the falling ball. above the horizontal with an initial
use different values of "t to see how
72. A golf ball is hit with an
velocity v at an angle �. Find
the average velocity approaches the
initial velocity v = 53.0 m/s at an
0 (a) the time t for the projectile to
r
instantaneous velocity. Compare
angle � = 50.00 above the horizontal. rise to its maximum height; (b) the
this to the velocity determined by
(a) How high will the ball go?
total time t the ball is in the air;
t
the equation v = at, and determine
(b) What is the total time the ball is
(c) the maximum distance the ball
the percentage error. Plot the
in the air? (c) How far will the ball
travels in the x-direction, x
max
average velocity, ("x)/("t), versus
travel horizontally before it hits the
before it hits the ground; (d) the
"t.
ground?
maximum height y of the
max
74. Free-fall and generalized
73. Instantaneous velocity. If
projectile; (e) the velocity v of the
g
one-dimensional projectile motion.
the equation for the displacement x
projectile as it strikes the ground;
A projectile is fired from a height y
of a body is known, the average
and (f) the location and velocity of
above the ground with an initial
velocity throughout an interval can
the projectile at any time t. (g) Plot
velocity v in a vertical direction.
be computed by the formula
a picture of the trajectory.
Find (a) the time t for the projectile
r
to rise to its maximum height,
v = ("x)/("t)
avg To go to these interactive
(b) the total time t the ball is in the
t
tutorials click on this sentence.
air, (c) the maximum height y of
max
The instantaneous velocity is
the projectile, (d) the velocity v of
g
defined as the limit of the average
the projectile as it strikes the
velocity as "t approaches zero. That
ground, and (e) the location and
is,
velocity of the projectile at any time
To go to another chapter, return to the table of contents by clicking on this sentence.
3-42 Mechanics [ Pobierz całość w formacie PDF ]

Wątki