Chapter 4 AP Set
1)Two people are in a boat that is capable of a maximum speed of 5 kilometers per hour in still water, and wish to cross a river 1-kilometer wide to a point directly across from their starting point. If the speed of the water in the river is 5 kilometers per hour, how much time is required for the crossing?
a) 1/20 hr b) 1/10 hr c) 1 hr d) 10 hr
e) The point directly across from the starting point cannot be reached under these conditions.
2)A projectile is fired from the surface of the Earth with a speed of 200 meters per second at an angle of 300 above the horizontal. If the ground is level, what is the maximum height reached by the projectile?
a) 5 meters b) 10 meters c) 500 meters d) 1,000 meters e) 2,000 meters
3) A ball of mass m is attached to the end of a string ------L------o------R
of length L as shown right. The ball is released from rest P
from position P, where the string is horizontal. It swings
through position Q, where the sting is vertical, and then to
position R, where the string is again horizontal. What are the
directions of the acceleration vectors of the ball at positions
Q and R?Q
POSITION QPOSITION R
a)downwarddownward
b)downwardto the right
c) upwarddownward
d)upwardto the left
e)to the rightto the left
4)A rock is dropped from the top of a 45 meter tower, and at the same time a ball is thrown from the top of the tower in a horizontal direction. Air resistance is negligible. The ball and the rock hit the level ground a distance of 30 meters apart. The horizontal velocity of the ball thrown was most nearly
a) 5 m/secb) 10 m/sec c) 14.1 m/sec d) 20 m/sec e) 28.3 m/sec
5)At a particular instant, a stationary observer on the ground sees a package falling with speed v1 at an angle to the vertical. To a pilot flying horizontally at constant speed relative to the ground, the package appears to be falling vertically with a speed v2 at that instant. What is the speed of the pilot relative to the ground?
a) v1 + v2b) v1 - v2c) v2 - v1d) v12 - v22e) v12 + v22
6) A balloon of mass M is floating motionless in the air. A person of mass less than M is on a rope ladder hanging from the balloon. The person begins to climb the ladder at a uniform speed v relative to the ground. How does the balloon move relative to the ground?
a) Up with speed vb) Up with a speed less than vc) Down with speed v
d) Down with a speed less than v e) The balloon does not move.
7) A spring-loaded gun can fire a projectile to a height h if it is fired straight up. If the same gun is pointed at an angle of 450 from the vertical, what maximum height can now be reached by the projectile?
a) h/4b) h/2(2)1/2c) h/2 d) h/(2)1/2e) h
8) A ball of mass m at one end of a string of length R rotates in a vertical circle just fast enough to keep the string from going slack when the ball is at the top of the circle. The ball/s speed when it is at the bottom of the circle is
a) (2gR) 1/2 b) (3gR) 1/2c) (4gR) 1/2d) (5gR) 1/2e) (7gR) 1/2
9) A projectile has an initial velocity of magnitude V0 P
which makes an angle 0 with the horizontal. Neglecting air friction,
all of the follow are true at point P, the highest point of its trajectory.
Except:
a)The time t required to reach P is given by t = v0 cos 0 / g
b)The horizontal displacement is v0 t cos 0, where t is the time required to reach P
c)Hmax = (v0 sin 0)2 / 2g
d)The speed is v0 cos 0
e)The acceleration is g.
10) A particle is moving in a circle of radius 2 meters according to the relation = 3t2 + 2t, where is measured in radians and t in seconds. Find its velocity at t = 4 seconds.
a) 13 m/sec b) 16 m/sec c) 26 m/sec d) 52 m/sec e) 338 m/sec
11) A racing car is moving around the circular track of radius 300 meters. At the instant when the car's velocity is directed due east, its acceleration is directed due south and has a magnitude of 3 meters per second squared. When viewed from above, the car is moving
a) clockwise at 30 m/sec b) clockwise at 10 m/sec c) counterclockwise at 30 m/sec
d) counterclockwise at 10 m/sec e) with constant velocity
12)A particle moves along the parabola with equation y = 1/2 x2 shown below.
a)Suppose the particle moves so that the x-component of its velocity has the constant value
vx = c; that is x = ct.
- On the diagram to the right, indicate the directions of the particle's velocity vector v and its acceleration vector a at the point R, and label each vector.
- Determine the y-component of the particle's velocity as a function of x.
- Determine the y-component of the particle's acceleration.
b)Suppose, instead, that the particle moves along the same parabola with a velocity whose x-component is given by vx = c / (1 + x2) 1/2
- Show the particle's speed is constant in this case.
- On the diagram indicate the directions of the particle's velocity vector v and acceleration vector a at point s, and label each vector. State the reason for your choices.
13. A pendulum (with string length “L”) and ball of mass “m” is pulled back to a horizontal position and
then released. Assuming that is the angle between the string and the vertical, find…
a) the speed of the ball(v) at an angle of as a function of m, g, L, and/or . This should be done using conservation of energy.
b) the magnitude of the radial acceleration (ar) of this ball at an angle of as a function of m, g, L, and/or .
c) the magnitude of the tangential acceleration (at) of this ball at an angle of as a function of m, g, L, and/or .
d)the magnitude of the TOTAL acceleration (a) of this ball at an angle of as a function of m, g, L, and/or .
e)the angle () associated with the TOTAL acceleration of this ball at an angle of as a function of m, g, L, and/or .
Plot each of the functions found in parts a thru e below and show how they vary with .