The position vector is obtained as r = 1.12 k + 0.58 i + 1.22 j.
What is the position?Let us consider the movement of the squirrel. We know that the position of the squirrel is defined by the equation; r⃗ =[(0.280m/s)t+(0.0360m/s2)t2]i^+(0.0190m/s3)t3j^. We can see that this equation is what defines the position of the squirrel in the three cartesian dimensions as shown in the question.
We now have the position as required at the instant where t = 4.00 s being obtained as; r⃗ =[(0.280m/s)(4)+(0.0360m/s2)(4^2) ]i+(0.0190m/s3)(4)^3j. We now finally obtain the position of the body as required as being;
r = 1.12 k + 0.58 i + 1.22 j
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A bicycle with 26-inch diameter wheels is traveling at 20 mi/h. Find the angular speed of the wheels in rad/min.
______radians per minute.
How many revolutions per minute do the wheels make?
___revolutions per minute
A bicycle with 26-inch diameter wheels is traveling at 20 mi/h. Find the angular speed of the wheels in rad/min.
______radians per minute
___revolutions per minuteω = 1320 rad/min, Revolution per minutes = 210.084
Diameter = 24 in
Radius r = 24/2 in = 12 in = 12 × 2.54 cm = 30.48 cm = 0.3048 m
Linear Speed v= 15 mi/hr = 15 * 1609.34 / 3600 m/s = 6.7056 m/s
Angular Speed ω = v / r = (6.7056 m/s) / (0.3048 m) = 21.999945
ω = 22 rad/s = 22× 60 rad/min = 1320 rad/min
∴ 1 revolution = 2π rad
⇒1 rad = 1 / 2π rev
so 1320 rad/min = 1320 / 2π rev/min = 210.0845 rev/min
Revolution per minutes = 210.0845
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A baseball player hits a pop fly ball. If the ball leaves the bat at 45 m/s at an angle of 68° above the horizontal, what is the maximum height above the point of contact with the bat that the ball will reach? Ignore air resistance.
The maximum height above the point of contact with the bat that the ball would reach would be 88.72 meters
What is a projectile motion?It is the movement of any item or body when it is launched from the the earth's surface and follows any curving course while being affected by the gravitational pull of the planet.
The maximum height of the projectile motion is given by,
Maximum height = v² sin²θ / 2 g
=45² sin² 68/ 2 *9.81
=88.72 meters
Thus, the maximum height the ball would reach would be 88.72 meters
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A football player has a mass of 100 kg and can accelerate at 4 m/s². How much
force does this football player apply?
Answer: F=400 N
Explanation:
F=ma ==> F=force, m=mass, a=acceleration
F=100*4
F=400 N
what is the general formula for measuring [tex] \vec{B} [/tex] , i.e. , magnetic field intensity ?
tysm ;-;
Explanation:
[tex]{ \rm{ \vec{B}} = \frac{ \mu_{0}N}{l} } \\ [/tex]
N is number of turns
l is conductor length
mu_0 is permeability
[tex]{ \boxed{ \tt{ \mu_{0} = 4\pi \times {10}^{ - 7} }}}[/tex]
#include <stdio.h>
int main()
{
const int LENGTH = 10;
const int WIDTH = 5;
const char NEWLINE = '\n';
int area;
area = LENGTH * WIDTH;
printf("value of area : %d", area);
printf("%c", NEWLINE);
return 0;
}
adding base ions to a soultion will make the soultion more
Adding base ions to a solution will make the solution more basic.
When base ions are added it indicates adding OH⁻ ions, which will increase the pH of the solution and hence free H⁺⁺ ions will be decreased which leads to the increase in basicity of the solution.
pH is a logarithmic measure of the concentration of hydrogen ions in an aqueous solution.
It defines how acidic or basic the solution is.The solution having pH value below 7 is considered as acidic and and a pH greater than 7 is basic.Solutions having pH value as 7 is called a neutral solution.Therefore if the base ions are added to the solution, pH of the solution will increase and hence it will become more basic.
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(c)
Another four students did the same experiment.
The measurements taken and the calculated values for power are given in the table.
Student
A
(ii)
B
C
D
Weight in
newtons
285
360
600
725
Time taken in Power in watts
seconds
3.8
2.4
3.4
4.0
240
480
560
580
(i)
To make a fair comparison of their powers the students kept one variable in the
experiment constant.
What variable did the students keep constant?
From the data in the table a student wrote the following conclusion.
'The greater the weight of the student the greater the power developed.'
Suggest why this conclusion may not be true for a larger group of students.
The early phases of undertaking an epidemiological, clinical, or lab study include calculating the sample size. There are ethical and methodological guidelines that should be followed when creating a scientific publication.
When it comes to making clinical judgments, two studies that used the same approach and produced equal results but had different sample sizes could provide the researcher with different information. Therefore, contrary to popular belief, samples should not be too tiny or too large in the perfect world. The primary effects of the sample size on study interpretation will be covered in this paper using clinical terminology. Although it can appear at first glance that methodological difficulties are the most important thing, particularly to clinicians.
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what is visual merchandising
Answer:Visual Merchandising is the practice in the retail industry of optimizing the presentation of product and services to better highlight their features and benefits. The purpose of such visual merchandising is to attract, engage, and motivate the customer towards making a purchase
Explanation:
u welcome
The speed of sound is measured to be 340 m/s on a certain day.
What is this in Kilometers per hour?? s/km/h=
Please help and explain how to do these types of problems in very confused!!!
Find the direction of vector A -> = ( 21m)x^ + ( -15m)y^ (in degrees)
Find the magnitude of vector A -> = (21m)x^ + (-15m)y^ (in meters)
Find the direction of vector B -> = (4.5m)x^ + (20m)y^ (in degrees)
Find the magnitude of vector B -> = (4.5m)x^ + (20m)y^ (in meters)
Find the direction of vector A-> + B -> (in degrees)
Find the magnitude of vector A-> + B -> (in meters)
Answer: ill do deeper reaseach because thats hard
Explanation:
In which physical state.is fire and sun?
Answer:
Fire is in plasma physical state. It contains both gaseous and moist fluidy substances.
[tex].[/tex]
Answer:
Both gas state and liquid state or vapor (plasma overall)
1. A UEFA BAll is vertically Thrown up with an 'ni-
tial velocity of 25mls. Calculate;
i maximum height
Answer:
maximum height,h=31.25m
Explanation:
when an object is thrown vertically upward, v=0.
using the formula, v²= u²+2gh.
since the object is thrown upwards, g= -10m/s
v²=u²-2gh
0²=25²- 2×10×h
0=625-20h
20h = 625
h=31.25m
An electron moves in the positive x-direction a distance of 2.39 m in 2.89⋅10-8 s, bounces off a moving proton, and then moves in the opposite direction a distance of 1.65 m in 3.37⋅10-8 s.
a) What is the average velocity of the electron over the entire time interval?
b) What is the average speed of the electron over the entire time interval?
The average velocity of the electron over the entire time interval is 1.182 x 10⁷ m/s.
The average speed of the electron over the entire time interval is 6.454 x 10⁷ m/s.
What is average velocity?
The average velocity of an object is the change in the displacement of the object with time.
average velocity = total displacement / total time of motion
average velocity = (final position - initial position)/total time
average velocity = (2.39 m - 1.65)/(2.89 x 10⁻⁸ + 3.37 x 10⁻⁸)
average velocity = 1.182 x 10⁷ m/s
What is average speed?The average speed of an object is ratio of total distance to total time of motion of the object.
average speed = (2.39 m + 1.65 m)/(2.89 x 10⁻⁸ + 3.37 x 10⁻⁸)
average speed = 6.454 x 10⁷ m/s
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If the car was initially traveling at 96 km/h and came to a stop in 5.0 s along a straight, level road, what was the magnitude of the average force applied to the passenger by the seatbelt? The shoulder strap seatbelt holds a 56kg passenger in place.
The average force exerted by seatbelts on the passenger is 1493.3N.
initial velocity of the car, u = 96km/h
time taken by the car, s = 5.0 sec
final velocity of the after coming to rest, v = 0
mass of the passenger, m = 56 kg
to find out the acceleration of the car we use equation of motion
v = u+ at
0 = 96km/h + ax 5s
a = - 96 x 18/5x5
a = -26.6m/s²
The deceleration of the car is 26.6 m/s²
The force exerted on the passenger by the backward action of the car is calculated as
F = ma
where
m is mass
a is acceleration
F = 56 x 26.6
F = 1493.3 N
Therefore, the average force exerted by seatbelts on the passenger is 1493.3N.
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WILL GIVE BRAINLIEST!!!!
How many revolutions around the Sun does Uranus complete by the time Jupiter finishes its orbit?
Answer:
0
Explanation:
it takes 84 years for Uranus to orbit the Sun. It only takes 12 years for Jupiter to orbit the Sun. So technically by the time that Jupiter finishes it's one, Uranus will not be able to even finish half of its orbit.
To win the game, a place kicker must kick a
football from a point 54 m (59.0544 yd) from
the goal, and the ball must clear the crossbar,
which is 3.05 m high. When kicked, the ball
leaves the ground with a speed of 26 m/s at
an angle of 32.6° from the horizontal.
The acceleration of gravity is 9.8 m/s².
By how much vertical distance does the ball
clear the crossbar?
Answer in units of m.
The vertical distance with which the ball clears the crossbar is given by x= 1.34m
We are given in the question that the distance between the kicking point of football and the goal is 54m (59.0544 yd), Height of crossbar is 3.05m, Speed of the ball when it leaves the ground is 26m/s at an angle of 32.6° from horizontal and the acceleration due to gravity is 9.8 m/s².
The ball will follow projectile motion when kicked and the equation for finding time in a projectile motion is given by:
t = d/vcosθ
=> t = 54/(26×cos32.6°)
=> t = 2.5 s
Now newton's second equation of motion for finding distance in y direction is given by:
S= ut - 1/2(at²)
S=(26sin32.6°)2.5 - 1/2(9.8×2.5²)
S= 4.39m
Therefore, the vertical distance with which the ball clears the crossbar is given by x= 4.39 - 3.05 = 1.34m
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A bicyclist riding northwest along a road at 16 mph feels the wind blowing directly to the east at 17 mph. What wind speed would someone measure if they were standing at rest next to the road? .
The correct answer 12.611 mph.
Cyclist traveling in a northwest direction at a speed of 16 mph. (Directed 45 degrees from the North)
Cycling speed is therefore 16 sin (45 o) in the direction of the north and 16 cos (45) in the direction of the west
Let's assume that this is located on a cartesian plane. Let the positive Y-axis be north and the positive X-axis be east.
Speed = [tex]V_c[/tex] = (-16/√2 i + 16/√2 j) mph
In relation to a cyclist, the wind speed is = [tex]V_{cw[/tex] = 17 i mph
Let, V_w thus,
[tex]V_{cw = V_w - V_c[/tex]
[tex]V_w = V_{cw + V_c[/tex]
[tex]V_w[/tex] = 17i + (-16/√2 i + 16/√2 j)
[tex]V_w[/tex] = (17 - 16/√2) i + 16/√2 j
[tex]V_w[/tex] = 5.6 i + 11.3 j
| [tex]V_w[/tex]| = 12.611
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A 0.15 kg arrow is shot at +44 m/s. It hits an apple (m = 0.49 kg), and goes through the apple, leaving with a velocity of +28 m/s.
What is the velocity of the apple after the arrow leaves it?
Can anyone help me solve this?
A free-falling item is one that is falling solely as a result of gravity, as was discovered in the previous section of this course. A free-falling object experiences a downward acceleration of 9.8 m/s/s (on Earth).
Its acceleration due to gravity is the acceleration that an object experiences as a result of gravitational force. M/s2 is its SI unit. Gravitational acceleration is a vector, meaning it has a magnitude and a direction. The universal gravitational constant, G, is unaffected by the type of particle, the medium separating the particles, or the passage of time. Because its value is consistent throughout the cosmos, it is referred to as "universal."
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What safety features are commonly found in the car’s interior? (2 pts)
Answer: Airbag
Explanation:
Provides safety to passengers during a collision.
Two buckeys of nails are hung one above the other and are pulled up to a roof by a rope. Each buckey has a mass of 5.0 kg. The tension in the rope connecting the buckets is 60 N. Calculate the applied force needed to lift both buckets up.
The applied force needed to lift both buckets up is 71 N.
Net force on the bucketsThe net force applied on the buckets is calculated as follows;
F(net) = F(T) + (-Fg)
where;
F(net) is the net forceF(T) is the tension in the ropeFg is the force of gravitySubstitute the given parameters and solve for the net force on the bucket.
F(net) = 60 N - (5 x 9.8)
F(net) = 60 N - 49 N
F(net) = 11 N
Applied force needed to lift the bucketThe force needed to lift the bucket = F(net) + F(T)
F(app) = 11 N + 60 N
F(app) = 71 N
Thus, the applied force needed to lift both buckets up is 71 N.
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Consider two vectors a and B and their resultant A+ B the magnitude of the vector a and b respectively 16.2 and 6 and they act at 140 each other
The magnitude of resultant vector R = A + B is 12.23 if the act at 140° to each other.
We know that,
A + B = √ ( A² + B² + 2AB cos θ )
Given that,
A = 16.2
B = 6
θ = 140°
A + B = √ ( 16.2² + 6² + ( 2 * 16.2 * 6 * cos 140° ) )
R = √ ( 262.44 + 36 - 148.91 )
R = √ 149.52
R = 12.23
The magnitude of a vector is the numeric value of a vector. It gives the individual values vectors along x, y and z axis.
Therefore, the magnitude of resultant vector is 12.23
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For the roller coaster shown below, a hydraulic catapult propels the car to the top of the ride, at a height of 405 ft. If the car and occupants weigh 1188 lb, what would be the potential energy of the loaded car at the top in joules?
If a hydraulic catapult propels the car to the top of the ride, at a height of 405 ft. If the car and occupants weigh 1188 lb, then the potential energy of the loaded car at the top would be 652542.68 Joules.
What is mechanical energy?Mechanical energy is the combination of all the energy in motion represented by total kinetic energy and the total stored energy in the system which is represented by total potential energy.
As given in the problem, for the roller coaster, a hydraulic catapult propels the car to the top of the ride, at a height of 405 ft. If the car and occupants weigh 1188 lb,
1 lb = 0.4536 Kg
1188 lb = 1188× 0.4536 Kg
=538.87 Kilograms
1 ft = 0.3048 meters
405 ft = 405×0.3048 meters
=123.44 meters
The potential energy of the loaded car at the top = mgh
=538.87×9.81×123.44
=652542.68 Joules
Thus, the potential energy of the loaded car would be 652542.68 Joules.
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What is the difference between a fourier transform and fourier transform pair
Answer:
[tex]{ \tt{X( \omega) = x(t)}}[/tex]
How much tension must a cable withstand if it is used to accelerate a 1000-kg car vertically upward at 0.60 m/s2 ?
Answer:
Approximately [tex]10410\; {\rm N}[/tex] (assuming that [tex]g = 9.81\; {\rm m \cdot s^{-2}}[/tex].)
Explanation:
There are two forces on this car:
Upward tension force from the cable, andDownward weight of the car (gravitational pull.)The net force on this car would be:
[tex](\text{net force}) = (\text{tension}) - (\text{weight})[/tex].
Rearrange to obtain:
[tex](\text{tension}) &= (\text{net force}) + (\text{weight})[/tex].
Let the mass of this car be [tex]m[/tex]. The weight of the car would be [tex]m\, g[/tex].
If the acceleration of the car is [tex]a[/tex], the net force on this car would be [tex]m\, a[/tex].
Thus:
[tex]\begin{aligned}(\text{tension}) &= (\text{net force}) + (\text{weight}) \\ &= m\, a + m\, g \\ &= (m)\, (a + g) \\ &= (1000\; {\rm kg}) \, (0.60\; {\rm m \cdot s^{-2}} + 9.81\; {\rm m\cdot s^{-2}}) \\ &\approx 10410\; {\rm N}\end{aligned}[/tex].
Pleaseee help me with this question!!!!!!!
A ball is dropped vertically from 15.3 meter height. If the acceleration due to gravity is given by 9.8 ms^-2, find the time it will take for the ball to hit the ground.
The time taken for the ball to hit the ground is 1.77 s
Data obtained from the questionFrom the questionn give above, the following data were obtained:
Height (h) = 15.3 mAcceleration due to gravity (g) = 9.8 m/s²Time (t) =? How to determine the time taken to fall to the groundThe time taken for the ball to fall to the ground can be obtained as follow:
h = ½gt²
15.3 = ½ × 9.8 × t²
15.3 = 4.9 × t²
Divide both side by 4.9
t² = 15.3 / 4.9
Take the square root of both side
t = √(15.3 / 4.9)
t = 1.77 s
Thus, we can conclude that: it will take the ball 1.77 s to fall to the ground.
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Can anyone help me with this question pleaseeeeee?????
You are driving to your friends' house to pick them up to go to the movie theatre. The movie starts in 40 minutes. It takes you 10 mins to drive to your friends', and from there 15 more minutes to drive to the theatre at 40 miles per hour. You figured that you will reach ten minutes before the start of the movie. You expected your friends to be ready by the time you reach their place. Unfortunately, they were playing games, and it took 20 minutes for all of you to head out again from there. How fast should you drive now to reach the theatre before the movie begins? Provide your answer in miles per hours.
One must drive at a speed of 62.5 miles per hour to reach the theatre at time.
Time movie starts in: 40 minutes
Time taken to drive to friend's house: 10 minutes
Time taken to drive to the theatre from friend's house: 15 minutes
Speed = 40 miles per hour
Using the formula to find the distance:
Speed = Distance/Time
40 = Distance/(15/60)
40*0.25 = Distance
10 miles is the distance from the friend's house to the theatre
Now, time taken by friends while playing games = 20 minutes
Time remaining = 40 - 10 - 20 = 10 minutes
The distance required to be covered in 10 minutes is 10 miles
Therefore, using the formula we get:
Speed = 10/(10/60)
Speed = 62.5 miles per hour
Hence, one should drive at a speed of 62.5 miles per hour to reach the theatre on time
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A graduated cylinder contains 20.0ml of water. After a rock is placed in the cylinder, the level rises as shown below. what is the volume of the rock
The volume of the rock, given the data is 14 mL (Option A)
Data obtained from the questionFrom the question given above, the following data were obtained:
Volume of water = 20 mLVolume of water + rock = 34 mLVolume of rock =?How to determine the volume of the rockThe volume of the rock can be obtained by calculating the displacement of the water when the rock was added. this can be obtained as follow:
Displacement of water = (Volume of water + rock) - (volume of water)
Displacement of water = 34 - 20
Displacement of water = 14 mL
Thus, the volume of the rock is 14 mL
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Complete question:
See attached photo
Carbon14 has half life of 5,730 years. If an archaeological sample has only one-fourth of the radioactivity of a similar sample from today how old is the archaeological sample
The age of the sample will be 11460 years.
The half-life of C-14 = 5730 years.
The half- life time is the time taken by the object to attain its position till the half of its initial value.
i.e after 5730 years only half of the C-14 carbon will exists.
To retain one-fourth of the sample, another cycle of 5730 years is required.
This means 2 half-lives should have passed to retain one-fourth of the sample.
so to calculate it's age
[tex]\frac{t}{\frac{t}{\frac{1}{2} } }[/tex] = 2
where t = the age of the sample
with t(1/2) = the half-life time of the sample = 5470 years
2 = the number of half- lives passed
therefore
[tex]\frac{t}{5730}[/tex] = 2
t = 2*5730 = 11460 years
When only one-fourth of the sample will remain, the age of the sample will be 11460 years
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At the mail racing championship in England, the winner moved at an average velocity of 2.4 mm/s [ford] for 140 s. Determine the winning snail's displacement during this time interval.
The displacement of the victorious snail will be 336.0mm .
The term displacement refers to a change in an object's position. It is a vector quantity and has a direction and magnitude .
We are given here,
Average velocity of snail = Δv = 2.4 mm/s
Time interval taken by snail = Δt = 140 s
The average velocity can be define as, the rate of change in displacement in the particular time interval of the object. The formula can be given as,
Δv = Δx / Δt
Where, Δv is the average velocity, Δx is the change in displacement, Δt is the time interval of an object. Unit can be written as meter/second.
Therefore, the displacement of snail during the race can be calculated by the relation i.e.
Δx = Δv × Δt
Thus , putting the values in above equation we get,
Δx = 2.4mm/s × 140s
Δx = 336.0 mm
Hence, the snail would move 336.0 mm in 140s.
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HELP ASAP!!!!!!
If a car goes along a straight road heading east and speeds up from 45 ft/s to 60 ft/s in 5 s, calculate the acceleration.
fus 2
a=
Note: If the speed were given in miles per hour, and the time were given in minutes, you could change the minutes to a
fraction of an hour and do the problem. The answer would be in miles/h².
Answer:
3ft/s²
Explanation:
[tex]a = \frac{60 - 45}{5} = 3ft \div {s}^{2} [/tex]