Positions and velocities of a metal ball released from rest when air resistance is negligible. Velocity is seen to increase linearly with time while displacement increases with time squared. Acceleration is a constant and is equal to gravitational acceleration.
Suppose the ball falls 1.0000 m in 0.45173 s. Assuming the ball is not affected by air resistance, what is the precise acceleration due to gravity at this location?
Strategy
Draw a sketch.
We need to solve for acceleration
. Note that in this case, displacement is downward and therefore negative, as is acceleration.
Solution
1. Identify the knowns.
;
;
;
.
2. Choose the equation that allows you to solve for
using the known values.
3. Substitute 0 for
and rearrange the equation to solve for
. Substituting 0 for
yields
Solving for
gives
4. Substitute known values yields
so, because
with the directions we have chosen,
Discussion
The negative value for
indicates that the gravitational acceleration is downward, as expected. We expect the value to be somewhere around the average value of
, so
makes sense. Since the data going into the calculation are relatively precise, this value for
is more precise than the average value of
; it represents the local value for the acceleration due to gravity.
A chunk of ice breaks off a glacier and falls 30.0 meters before it hits the water. Assuming it falls freely (there is no air resistance), how long does it take to hit the water?
We know that initial position
, final position
, and
. We can then use the equation
to solve for
. Inserting
, we obtain
where we take the positive value as the physically relevant answer. Thus, it takes about 2.5 seconds for the piece of ice to hit the water.
Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (e.g.
) to see how they add to generate the polynomial curve.
An object in free-fall experiences constant acceleration if air resistance is negligible.
On Earth, all free-falling objects have an acceleration due to gravity
, which averages
Whether the acceleration
a should be taken as
or
is determined by your choice of coordinate system. If you choose the upward direction as positive,
is negative. In the opposite case,
is positive. Since acceleration is constant, the kinematic equations above can be applied with the appropriate
or
substituted for
.
For objects in free-fall, up is normally taken as positive for displacement, velocity, and acceleration.
Conceptual questions
What is the acceleration of a rock thrown straight upward on the way up? At the top of its flight? On the way down?
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
