A ball is launched at an angle of 60 degrees above the horizontal, and the vertical position of the ball is recorded at various points in time in the table shown, assuming the ball was at a height of 0 at time t = 0.
Draw a graph of the ball's vertical velocity versus time.
Describe the graph of the ball's horizontal velocity.
Draw a graph of the ball's vertical acceleration versus time.
The graph of the ball's vertical velocity over time should begin at 4.90 m/s during the time interval 0 - 0.1 sec (there should be a data point at t = 0.05 sec, v = 4.90 m/s). It should then have a slope of -9.8 m/s
2 , crossing through v = 0 at t = 0.55 sec and ending at v = -0.98 m/s at t = 0.65 sec.
The graph of the ball's horizontal velocity would be a constant positive value, a flat horizontal line at some positive velocity from t = 0 until t = 0.7 sec.
Summary
The
graphical method of adding vectors
and
involves drawing vectors on a graph and adding them using the head-to-tail method. The resultant vector
is defined such that
. The magnitude and direction of
are then determined with a ruler and protractor, respectively.
The
graphical method of subtracting vector
from
involves adding the opposite of vector
, which is defined as
. In this case,
. Then, the head-to-tail method of addition is followed in the usual way to obtain the resultant vector
.
Addition of vectors is
commutative such that
.
The
head-to-tail method of adding vectors involves drawing the first vector on a graph and then placing the tail of each subsequent vector at the head of the previous vector. The resultant vector is then drawn from the tail of the first vector to the head of the final vector.
If a vector
is multiplied by a scalar quantity
, the magnitude of the product is given by
. If
is positive, the direction of the product points in the same direction as
; if
is negative, the direction of the product points in the opposite direction as
.
Conceptual questions
Which of the following is a vector: a person's height, the altitude on Mt. Everest, the age of the Earth, the boiling point of water, the cost of this book, the Earth's population, the acceleration of gravity?
Give a specific example of a vector, stating its magnitude, units, and direction.
What do vectors and scalars have in common? How do they differ?
Two campers in a national park hike from their cabin to the same spot on a lake, each taking a different path, as illustrated below. The total distance traveled along Path 1 is 7.5 km, and that along Path 2 is 8.2 km. What is the final displacement of each camper?
If an airplane pilot is told to fly 123 km in a straight line to get from San Francisco to Sacramento, explain why he could end up anywhere on the circle shown in
[link] . What other information would he need to get to Sacramento?
Suppose you take two steps
and
(that is, two nonzero displacements). Under what circumstances can you end up at your starting point? More generally, under what circumstances can two nonzero vectors add to give zero? Is the maximum distance you can end up from the starting point
the sum of the lengths of the two steps?
Anatomy is the study of internal structure of an organism while physiology is the study of the function/relationship of the body organs working together as a system in an organism.
It depends on the type of infection. Bacterial, fungal, parasitic or viral?
schler
if you can share the sign ad symptoms of the skin infection then u geh the treatment cox they're different sign ad symptoms of skin infection with different treatment
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
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Source:
OpenStax, Sample chapters: openstax college physics for ap® courses. OpenStax CNX. Oct 23, 2015 Download for free at http://legacy.cnx.org/content/col11896/1.9
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