Answer:
The velocity of the second ball is approximately 2.588 m/s
The angle direction of the second ball is 75° counterclockwise from the horizontal
Explanation:
The initial velocity of the first billiard ball = 5 m/s
The initial velocity of the billiard ball the first billiard ball strikes = 0 m/s
The final velocity of the first billiard ball = 4.35 m/s
The final direction of motion of the first billiard ball = 30° below its original motion
For perfectly elastic collision, whereby the target is at rest initially, by conservation of momentum, we have;
m₁ × [tex]\underset{v_1}{\rightarrow}[/tex] = m₁·[tex]\underset{v'_1}{\rightarrow}[/tex] + m₂·[tex]\underset{v'_2}{\rightarrow}[/tex]
Which gives;
m₁ × 5·i = m₁·((√3)/2×5·i - 2.5·j) + m₂·[tex]\underset{v'_2}{\rightarrow}[/tex]
∴ m₂·[tex]\underset{v'_2}{\rightarrow}[/tex] = m₁ × 5·i - m₁·((√3)/2×5·i - 2.5·j)
m₂·[tex]\underset{v'_2}{\rightarrow}[/tex] = m₁ × 5·(1 - √3/2)·i + m₁·2.5·j = m₁ × 2.5·(2 - √3)·i + m₁·2.5·j
Therefore, given that the mass of both billiard balls are equal, we have, m₁ = m₂, which gives;
m₂·[tex]\underset{v'_2}{\rightarrow}[/tex] = m₁·[tex]\underset{v'_2}{\rightarrow}[/tex] = m₁ × 2.5·(2 - √3)·i + m₁·2.5·j
∴ [tex]\underset{v'_2}{\rightarrow}[/tex] = 2.5·(2 - √3)·i + 2.5·j
The magnitude of the velocity of the second ball is [tex]\underset{v'_2}{\rightarrow}[/tex] = √((2.5·(2 - √3))² + 2.5²) ≈ 2.588 m/s
The direction of the second ball, θ = arctan(2.5/((2.5·(2 - √3))) = 75° counterclockwise from the horizontal.
A meter stick is found to balance at the 49.7-cm mark when placed on a fulcrum. When a 41.5-gram mass is attached at the 28.5-cm mark, the fulcrum must be moved to the 39.2-cm mark for balance. What is the mass of the meter stick
Answer:
The value is [tex]M = 42.3 \ kg[/tex]
Explanation:
From the question we are told that
The first position of the fulcrum is x = 49.7 cm
The mass attached is [tex]m = 41.5 \ g[/tex]
The position of the attachment is [tex]x_1 = 28.5 \ cm[/tex]
The second position of the fulcrum is [tex]x_2 = 39.2 \ cm[/tex]
Generally the sum of clockwise torque = sum of anti - clockwise torque
So
[tex]CWT = m (x_2 - x_1)[/tex]
Here CWT stands for clockwise torque
[tex]ACWT = M ( x - x_2)[/tex]
So
[tex]m (x_2 - x_1) = M ( x - x_2)[/tex]
=> [tex]41.5 (39.2 - 28.5 ) = M ( 49.7 -39.2 )[/tex]
=> [tex]M = 42.3 \ kg[/tex]
How long will it take a sample of I-131 to decay to 12.5% assuming it's half-life is 8.07 days?
Answer:
If you take A0 to be the initial sample of iodine-131, you will be left with. 12⋅A0=A02→ ... m24 hours=12.5%mo=12.5⋅10−2⋅mo
Explanation:
is that what u look for
Sample I-131 decays to 12.5% in 24.21 days.
What is half-life?Half-life, in radioactivity, is the amount of time needed for half of a radioactive sample's atomic nuclei to decay (change spontaneously into other nuclear species by emitting particles and energy), or, alternatively, the amount of time needed for a radioactive material's rate of disintegrations per second to decrease by half.
Give parameters:
Half-life of the radioactive element I-131:T = 8.07 day
It decays to 12.5% means it decays to 1/8.
According to definition of half-life,
The radioactive element I-131 decays to half in 8.07 days.
So, the radioactive element I-131 decays to 1/8 in 3×8.07 days = 24.21 days.
Hence, the radioactive element I-131 decays to12.5% in 24.21 days.
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Give one example where friction is useful. Can someone feed me with correct answer pls c:
Answer:
Friction is what holds your shoe to the ground. The friction present on the ice is very little, this is the reason why it is hard to walk on the slippery surface of the ice.
Explanation:
Why do women typically tend to have slightly greater stability than men?
A.
Women are shorter than men, and shorter people are more stable.
B.
Men have more muscle mass in their lower bodies that makes them stiff and less stable.
C.
Women have lower centers of gravity, and lower centers of gravity provide more stability.
D.
The increased muscle mass in their upper bodies makes their centers of gravity difficult to find.
Please select the best answer from the choices provided.
A
B
C
D
Answer:
C
Explanation:
I figured it sounded more accurate
A car is traveling with 90km/hr and another car with 20m/s in opposite direction. Calculate the relative velocity.
Answer:
Vba = -20 m/s - 25 m/s = -45 m/s
Vab = 25 m/s + 20 m/s = 45 m/s
Explanation:
Relative Velocity
The relative velocity of object B with respect to object A (Vba) measures the velocity of B in the rest frame of object A.
It's calculated as:
Vba = Vb - Va
The velocity of car B is Vb=-20 m/s and the velocity of car A is Va=90 Km/h.
Converting Va to m/s:
Va = 90 Km/h * 1000/3600 = 25 m/s
Thus, the relative velocity of B with respect to A is:
Vba = -20 m/s - 25 m/s = -45 m/s
And the relative velocity of A with respect to B is:
Vab = 25 m/s + 20 m/s = 45 m/s
mass does not vary from place to place why?
Answer:
It is always constant unlike weight
True or False? Will mark Brainlest
Answer:
False
Explanation:
They had no free oxygen though they has oceans forming and it was very hot and today is much different hope that helps!
A go-cart and rider have a mass of 14 kg. If the cart accelerates at 6m/s^2 during a 40 m sprint in 100 seconds, how much power did the cart do? MUST SHOW ALL WORK!!!!!!!!!
Answer:
P = 33.6 [N]
Explanation:
To solve this problem we must use Newton's second law, which tells us that the sum of forces on a body is equal to the product of mass by acceleration.
∑F = m*a
where:
F = forces [N]
m = mass = 14 [kg]
a = acceleration = 6 [m/s²]
[tex]F = 14*6\\F = 84 [N][/tex]
In the second part of this problem we must find the work done, where the work in physics is known as the product of force by distance, it is important to make it clear that force must be applied in the direction of movement.
[tex]W = F*d[/tex]
where:
W = work [J]
F = force = 84 [N]
d = displaciment = 40 [m]
[tex]W = 84*40\\W = 3360 [J][/tex]
Finally, the power can be calculated by the relationship between the work performed in a given time interval.
[tex]P=W/t\\[/tex]
where:
P = power [W]
W = work = 3360 [J]
t = time = 100 [s]
Now replacing:
[tex]P=3360/100\\P=33.6[W][/tex]
The power is given in watts
A pinball bangs against a bumper of a pinball machine with a speed of 0.9 m/s. If the ball has a mass of 0.056 kg, what is the ball's kinetic energy?
A softball pitcher rotates a 0.250 kg ball around a vertical circular path of radius 0.5 m before releasing it. The pitcher exerts a 33.0 N force directed parallel to the motion of the ball around the complete circular path. The speed of the ball at the top of the circle is 13.0 m/s. If the ball is released at the bottom of the circle, what is its speed upon release
Answer:
The value is [tex]u = 27.93 \ m/s[/tex]
Explanation:
From the question we are told that
The mass of the ball is [tex]m = 0.250 \ kg[/tex]
The radius of the circle is [tex]r = 0.5 \ m[/tex]
The force exerted is [tex]F = 33 \ N[/tex]
The speed of the ball on top of the circle is [tex]v = 13.0 \ m/s[/tex]
Gnerally from the law of energy conservation we have that
[tex]PE + W = \Delta KE[/tex]
Here PE is the potential energy of the pitcher which is mathematically represented as
[tex]PE = m * g * (2 r )[/tex]
=> [tex]PE = 0.250 * 9.8 * (2 * 0.5 )[/tex]
=> [tex]PE = 24.5\ J[/tex]
And W is the workdone by the force applied which is mathematically represented as
[tex]W = F * \pi * r[/tex]
=> [tex]W = 33 * 3.142 * 0.5[/tex]
=> [tex]W = 51.84 \ J[/tex]
And [tex]\Delta KE[/tex] is the change in kinetic energy which is mathematically represented as
[tex]\Delta KE = \frac{1}{2} * m * (v^2 - u^2 )[/tex]
=> [tex]\Delta KE = \frac{1}{2} * 0.250 * ( 13^2 - u^2 )[/tex]
=> [tex]\Delta KE = 0.125 * ( 13^2 - u^2 )[/tex]
=> [tex]\Delta KE = 21.125 - 0.125u^2[/tex]
So
[tex]24.5 + 51.84 = 21.125 - 0.125u^2[/tex]
=> [tex]u = 27.93 \ m/s[/tex]
The velocity of the ball released at the bottom is required.
The velocity of the ball released at the bottom is 24.56 m/s
F = Force = 33 N
r = Radius of loop = 0.5 m
m = Mass of ball = 0.25 kg
u = Initial velocity of ball = 13 m/s
v = Final velocity
g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]
The energy balance of the system is given by
[tex]F\pi r+mg2r=\dfrac{1}{2}m(v^2-u^2)\\\Rightarrow v=\sqrt{\dfrac{2}{m}(F\pi r+mg2r)+u^2}\\\Rightarrow v=\sqrt{\dfrac{2}{0.25}(33\times \pi\times 0.5+0.25\times 9.81\times 2\times 0.5)+13^2}\\\Rightarrow v=24.56\ \text{m/s}[/tex]
The velocity of the ball released at the bottom is 24.56 m/s.
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13. Austin rode his bike 10 m/s for two minutes. How far did he travel? A. 200 meters B. 1200 meters C. 1000 meters D. 20 meters
Answer:
B. 1200
Explanation:
60 sec in one min in 2 min there will be 120 sec. 10x120=1200
Jerry is pushing a 50-kg box across a moth floor with an acceleration of 0.6 m/s2. What force is he applying to the box? *
83.3 N
0.012 N
0
30 N
Answer:
30 NExplanation:
The force acting on an object given it's mass and acceleration can be found by using the formula
force = mass × acceleration
From the question we have
force = 50 × 0.6
We have the final answer as
30 NHope this helps you
what are the effects of moon rotation and revolution
Answer:
The effects of the Moon's rotation includes;
1) The Moon rotation and revolution gives the appearance of a perfectly still Moon to observers of the Moon from the Earth
2) The Moon has two sides, the near side that continuously faces the Earth and the "back" or far side, which is also known as the dark side of the Moon
The effect of the Moon's revolution
1) The tides in the ocean and water bodies, due to the gravitational forces from the Moon
2) The changes in the observed shape of the Moon due to the amount of Sunlight that is able to be reflected from the Moon as a result of the relative position of the Moon, the Earth and the Sun, at a given point in time
3) Lunar and Solar eclipse, when the Earth and the Moon blocks the light coming from the Sun respectively, due to their combined revolution
Explanation:
The duration of the Moon's orbit round the Earth = 27.322 days
The time it takes the Moon to rotate round its axis = 27 days
The Moon is the closest cosmic body to the Earth.
It takes serina 0.25 hours to drive to school. Her route is 16km long . What is serina’s average speed on her drive to school
Explanation:
distance=16km=16000m
time=0.25hours=1/4hr=15min=900sec
speed=dist./time
=16000/900=160/9=17.777m/s
speed=17.78m/s (rounded)
Answer:
64
Explanation:
Avg. speed = total distance/total time
Avg. speed= 16km/0.25h
Avg. speed= 64km/h
A child kicks a ball horizontally with a speed of 4.8 m/s off a deck 3.5 m off the
ground. How long will it take, in seconds, for the ball to hit the ground?
Answer:
0.73 sExplanation:
The time taken can be found by using the formula
[tex] t = \frac{d}{v} \\ [/tex]
d is the distance
v is the velocity
From the question we have
[tex]t = \frac{3.5}{4.8} \\ = 0.72916...[/tex]
We have the final answer as
0.73 sHope this helps you
a car travelling at 20 ms-1 accelerates uniformly for 8 s until its velocity reaches 36 ms-1.what are the acceleration and the average velocity of the car during this period
Answer:
Acceleration of the car = 2 m/s²
Average velocity of the car =28 m/s
Explanation:
Initial velocity = 20 m/s
Final velocity = 36 m/s
Time taken = 8 s
Acceleration = Δ velocity / time taken
Acceleration = 36-20 / 8 = 16/8 = 2 m/s²
Average velocity of the car =[ Initial velocity + Final velocity ] /2
Average velocity of the car = [ 20+36] / 2 = 28 m/s
How are seeds different from spores?
Seeds have endosperm which provides nourishment for a new plant, but spores do not have any stored food supplies.
Spores have an endosperm and involve sperm and egg cells, while seeds do not.
Spores involve egg and sperm cells, while seeds do not.
Spores will germinate and must find good soil to survive. Seeds can survive in extremely harsh conditions.
Explanation:
1.Seeds have endosperm which provides nourishment for a new plant, but spores do not have any stored food supplies.
hope it helpful
A projectile is fired into the air. Three characteristics of its subsequent motion are
1) the horizontal component of velocity
II) the vertical component of velocity
III) the acceleration
Neglecting air resistance, which characteristic(s) change(s) whilst the projectile is in the air.
(1 Point)
I only
Il only
II and III only
I and II only
Answer:
The answer is C) II and III only
Explanation:
HELP ASAP!! WILL TRY TO GIVE BRAINLIESTT!!
Please define the prefixes hyper-, hypo-, & iso- AND describe a solution that is hypertonic, hypotonic, & isotonic as well as compare how a living cell reacts when placed in a solution of each of the 3 types.
If a cell is placed in a hypertonic solution, water will leave the cell, and the cell will shrink. In an isotonic environment, there is no net water movement, so there is no change in the size of the cell. When a cell is placed in a hypotonic environment, water will enter the cell, and the cell will swell.
2. Heavier football players tend to play on the front line. Why?
What law is it?
Answer: They are put in front for defense so so they can block the opponents from getting the ball
Explanation:
Answer:
Heavier football players are usually on the front line because they have a low point in gravity therefore they are able to block the back running players in a better way. And its Newton's second law.
Explanation:
Beth moves a 15 N book 20 meters in 10 seconds. How much power was produced?
Answer:
30 Watts
Explanation:
Power = Work/Time
Work = Force*Distance
Power = Force * Distance / Time
Power = 15 N * 20 meters / 10 sec
Power = 30 Watts
what phenomenon reduces the adverse effects and pressure imposed by solar wind on earth?
Answer:
The earths magnetic field
Explanation:
Which of the following is most likely to be a conductor?
OA. Aplastic
OB. A molecule containing only nonmetal atoms
OC. A covalently bonded molecule
D. Acompound containing metallic bonds
Answer:
D.
Explanation:
A compound containing metallic bonds
hope it helps!
While delivering 125 kg blocks of ice to a local village, Kristoff and his family (and Sven too) come upon a cliff that is 5.7 m above them. To solve their problem, they build a catapult that will launch their blocks of ice with an initial velocity of 15 m/s and at an angle of 45 degrees above the ground.
Prove that the catapult will successfully launch the ice blocks up to the top of the cliff. Quantities you will need to solve for will be initial vertical velocity, horizontal velocity, the distance the catapult is from the cliff, and the amount of time it takes the ice to reach the cliff. Assume that they are experts and have arranged everything so that the ice blocks just barely reach the top of their parabolic path when they land at the top of the cliff and make a smooth landing. Draw a picture of the scene to help you visualize what is happening.
After landing on the flat land above, each block of ice travels 20 meters while slowing to a stop.
What is the rate of acceleration while the blocks slow to a stop?
How long do the blocks take to slow to a stop?
What is the amount of friction between the ice and the snowy ground?
How long do the blocks take to slow to a stop?
What is the amount of friction between the ice and the snowy ground?
Answer:
a. Since h = 5.74 m > 5.7 m, the height of the cliff, the block of ice will successfully launch to the top of the cliff.
b. -2.81 m/s²
c. 3.78 s
d. -351.25 N
Explanation:
a. After landing on the flat land above, each block of ice travels 20 meters while slowing to a stop.
For the block of ice to reach the top of the cliff, its maximum height, h should be greater than or equal to 5.7 m. That is, h ≥ 5.7 m.
The maximum height of a projection h, projected with an initial velocity v at an angle Ф is h = v²sin²Ф/2g where g = acceleration due to gravity = 9.8 m/s².
For the block of ice, v = 15 m/s and Ф = 45°. So,
h = v²sin²Ф/2g
= (15 m/s)²sin²45/(2 × 9.8 m/s²)
= 225 (m/s)²(1/√2)²/19.6 m/s²
= 225 (m/s)²(1/2)/19.6 m/s²
= 112.5 (m/s)²/19.6 m/s²
= 5.74 m
Since h = 5.74 m > 5.7 m, the height of the cliff, the block of ice will successfully launch to the top of the cliff.
The graph is in the attachment.
b. What is the rate of acceleration while the blocks slow to a stop?
Using v² = u² + 2as where u = initial horizontal velocity of block = 15m/scos45° = 10.61 m/s, v = final velocity of block = 0 m/s since it stops, a = acceleration and s = distance block moves = 20 m
So, a = (v² - u²)/2s
substituting the variables into the equation, we have
a = ((0 m/s)² - (10.61 m/s)²)/2(20 m)
= - 112.57 (m/s)²)/40 m
= -2.81 m/s²
c. How long do the blocks take to slow to a stop?
Using v = u + at where u = initial horizontal velocity of block = 10.61 m/s v = final velocity of block = 0 m/s since it stops, a = acceleration = -2.81 m/s² and t = time it takes block of ice to stop
So, making t subject of the formula,
t = (v - u)/a
substituting the values of the variables, we have
t = ( 0 m/s - 10.61 m/s)/-2.81 m/s²
= -10.61 m/s/-2.81 m/s²
= 3.78 s
d. What is the amount of friction between the ice and the snowy ground?
The frictional force, f = net force on block of ice
f = ma where m = mass of bock = 125 kg and a = acceleration of block = -2.81 m/s²
f = ma
= 125 kg(2.81 m/s²)
= -351.25 N
The photograph shows matter going through a physical change. Which characteristic of the matter changes?
A. shape.
B. shininess.
C. state.
D. type of atoms
Answer:
Possibly shape.
Explanation:
Because it is ripped in half. As you guys and the questioner can see that there is a wiggly strip down the middle. That also cause of a shape change.
I really hope my answer is right ^_^
The characteristic of matter which is undergoing change in the picture is it's shape as it is being teared apart.
What is matter?Matter in chemistry, is defined as any kind of substance that has mass and occupies space that means it has volume .Matter is composed up of atoms which may or not be of same type.
Atoms are further made up of sub atomic particles which are the protons ,neutrons and the electrons .The matter can exist in various states such as solids, liquids and gases depending on the conditions of temperature and pressure.
The states of matter are inter convertible into each other by changing the parameters of temperature and pressure.Matter possesses both particle and wave characteristics.Phase is a form of matter having uniform composition as well as physical properties.
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How much would a pair of 0.5 kg shoes weigh on Earth? (Include units in
your answer) *
Answer:
1.1 lbs
Explanation:
To convert kg to lbs you multiply kilograms by 2.2. So 0.5kg × 2.2 equals to 1.1 lbs
A 0.15 kg ball is moving with a velocity of
35 m/s. Find the momentum of the ball.
Answer:
5.25 kg.m/sExplanation:
The momentum of an object can be found by using the formula
momentum = mass × velocity
From the question we have
momentum = 0.15 × 35
We have the final answer as
5.25 kg.m/sHope this helps you
n Olympic diver is on a diving platform 3.60 m above the water. To start her dive, she runs off of the platform with a speed of 1.3 m/s in the horizontal direction. What is the diver's speed, in m/s, just before she enters the water
Answer:
8.5m/s
Explanation:
Using the equation of motion
v² = u² + 2gH
v is the final speed of the diver
u is the initial speed of the diver
g is the acceleration due to gravity
H is the height of the object
Given the following
V = 1.3m/s
H = 3.60m
g = 9.8m/s²
Required
Initial speed of the diver u
Substitute the given values into the formula:
v² = u² -2gH
1.3² = u² - 2(9.8)(3.60)
1.69 = u²-70.56
u² = 1.69+70.56
u² = 72.25
u = √72.25
u = 8.5m/s
Hence the diver's speed, in m/s, just before she enters the water is 8.5m/s
What is the height of a horizontal projectile if it takes 3 seconds to hit the ground?
a
29.4 m
b
3.0 m
C
44.1 m
d
88.3 m
Answer:
B
Explanation:
what is gravity???☺️
Answer:
Gravity
Explanation:
its an invisible force that pulls objects
toward each other.
hope it helps