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Homework assignment 3 (covers Sections 3.1, 3.2, 3.3, 3.4, 3.5)
Due: 2:00am on Monday, April 19, 2010
Note:
You will receive no credit for late submissions.
To learn more, read your instructor's
Grading Policy
First review Sections 3.1, 3.2, 3.3, 3.4, and 3.5 of Young and Freedman,
including
the worked examples. You should then be able to
solve the problems given below.
Note
that you are allowed only 6 answer attempts per problem.
Conceptual Problem about Projectile Motion
Description:
Conceptual questions about speed, peak characteristics, flight time, and range for an object undergoing projectile
motion.
Learning Goal:
To understand projectile motion by considering horizontal constant velocity motion and vertical constant
acceleration motion independently.
Projectile motion
refers to the motion of unpowered objects (called projectiles) such as balls or stones moving near the surface of
the earth under the influence of the earth's gravity alone. In this analysis we assume that air resistance can be neglected.
An object undergoing projectile motion near the surface of the earth obeys the following rules:
1. An object undergoing projectile motion travels horizontally at a constant rate. That is, the
x
component of its velocity,
, is constant.
2. An object undergoing projectile motion moves vertically with a constant downward acceleration whose magnitude,
denoted by
, is equal to 9.80
near the surface of the earth. Hence, the
y
component of its velocity,
, changes
continuously.
3. An object undergoing projectile motion will undergo the horizontal and vertical motions described above from the instant
it is launched until the instant it strikes the ground again. Even though the horizontal and vertical motions can be treated
independently, they are related by the fact that they occur for exactly the same amount of time, namely the time
the
projectile is in the air.
The figure shows the trajectory (i.e., the path) of a ball
undergoing projectile motion over level ground. The time
corresponds to the moment just after the ball is launched
from position
and
. Its launch velocity, also
called the initial velocity, is
.
Two other points along the trajectory are indicated in the figure.
One is the moment the ball reaches the peak of its
trajectory, at time
with velocity
. Its position at this
moment is denoted by
or
since it is at
its maximum height.
The other point, at time
with velocity
, corresponds
to the moment just before the ball strikes the ground on
the way back down. At this time its position is
,
also known as (
since it is at its maximum horizontal range.
Projectile motion is symmetric about the peak, provided the object lands at the same vertical height from which is was

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