The resultant velocity of the man is 12.5 m/s N of E.
Velocity of the man, Vm = 7.5 m/s
Velocity of Ship, Vs= 10 m/s
Since, velocity is a vector quantity, it will have both the magnitude and the direction.
So the magnitude for the resultant vector can be calculated by using the formula
[tex]\sqrt{x^{2} +y^{2} }[/tex] ; where x is the magnitude of the x-axis component and y is the magnitude of the y-axis component
i.e.
= [tex]\sqrt{Vm^{2} +Vs^{2} }[/tex]
= [tex]\sqrt{7.5^{2} + 10^{2} }[/tex]
= [tex]\sqrt{156.25}[/tex]
= 12.5 m/s
Also the direction can be calculated by Tan[tex]\alpha[/tex]
Tan[tex]\alpha[/tex] = [tex]\frac{10}{7.5}[/tex]
= Tan⁻(1.33)
= 58.9°
The angle between the resultant velocity and the horizontal axis is 58.9°.
Therefore the resultant velocity of the man relative to the water is 12.5 m/s towards NORTH-EAST direction.
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What is the difference between a fourier transform and fourier transform pair
Answer:
[tex]{ \tt{X( \omega) = x(t)}}[/tex]
Are mass and energy conserved?
The conservation of mass and energy just means that they can't be destroyed, only changed into other forms. For example, when we burn something, the matter isn't going away. It is just changing into heat and light energy. After any chemical reaction, the amount of matter and energy will stay the same.
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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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
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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An air-conditioning unit is fastened to a roof that slopes at an angle of θ = 39 ∘ above the horizontal (Figure 1). Its weight is a force F⃗ on the air conditioner that is directed vertically downward. In order that the unit not crush the roof tiles, the component of the unit’s weight perpendicular to the roof cannot exceed 435 N. (One newton, or 1 N, is the SI unit of force. It is equal to 0.2248 lb.) (a) What is the maximum allowed weight of the unit? (b) If the fasteners fail, the unit slides L = 1.30 m along the roof before it comes to a halt against a ledge. How much work does the weight force do on the unit during its slide if the unit has the weight calculated in part (a)? The work done by a force F⃗ on an object that undergoes a displacement s⃗ is W=F⃗ ⋅s⃗ .
A) the maximum weight of the air-conditioning unit allowed is 557.7 N. and B) the work done by force F on the object that undergoes displacement is 456.75 J.
Given in the question,
The angle of the Slope = 39 Degrees
Max Weight perpendicular of the roof allowed = 435 N
Distance of roof = 1.3 meters
Let us assume the force of the weight of air-conditioning unit be F.
Now as the roof is at the slope of 39 degrees, The weight perpendicular to the roof tile will be the cos component of the force F.
Max perpendicular Weight = F×(cos(Ф)),
Put in the values, we get
F × Cos(39) = 435
F = 435/Cos(39)
F = 435/0.78 [ Value of cos39 = 0.78 ]
F = 557.7 N
a) So, the maximum weight of the air-conditioning unit allowed is 557.7 N.
b) If the unit sides down the roof, the vertical distance traveled by the unit will be the sin component of the length traveled by it along the roof.
Vertical Displacement = (Length Along Roof)× Sin(39)
Force vertically Downward = F = 557.7 N
Using Formula, W= F.s, Put in the value, we get
W = F × (Length Along Roof)× Sin(39)
W = 557.7 × 1.3 × 0.63
W = 456.75 J
So, A) the maximum weight of the air-conditioning unit allowed is 557.7 N. and B) the work done by force F on the object that undergoes displacement is 456.75 J.
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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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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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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
Find the distance between the tips (ends) of the Minute Hand and the Hour Hand. The Minute Hand has a length of 17.0 ft. The Hour Hand has a length of11.0 ft.
The distance between the hands is obtained as 13 ft.
What is the distance between them?Let us commence by restating the definition of distance as the difference between two points. Now from the image we can see the geometry of the problem. The minute hand is clearly much longer than the hour hand we can not solve this problem if we do not involve the Pythagoras theorem seeing that a right angled triangle has to be formed in this case here.
Length of the minute hand = 17.0 ft
Length of the hour hand = 11.0 ft
Using the Pythagoras theorem;
c^2 = a^2 + b^2
b^2 = c^2 - a^2
b = √c^2 - a^2
b = √(17.0)^2 - (11)^2
b = 13 ft
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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
Question 1. A ball thrown upward at 5.1 m/s, what is the balls speed 4.9 seconds after it leaves the person's hand? (g=+9.80 m/s/s)
Question 2. (Vf2 = Vo2 +2ad) Using the above equation, a ball launched upward at 45 m/s. What height does the ball get to when the speed is 8 m/s upward?
Question 3. I water balloon is initially launched at 55 m/s upward. How fast will the balloon be traveling at when it first gets to a height of 64 meters above the ground?
(F.O.R g = -9.80 m/s/s)
Explanation:
what K what is k What is Q what is 8Consider 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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What magnitude charge creates a 4.70 N/C electric field at a point 3.20 m away?
The charge is obtained as 5.35 * 10^-9 C.
What is the electric field?The electric filed is defined as the region in space where the influence of a charge is felt. In this case, we know that the magnitude of the electric charge has been given to be 4.70 N/C and the distance is 3.20 m.
Let us recall that;
E = Kq/r^2
K = electric field constant
q = magnitude of charge
r = distance of separation
E = Kq/r^2
Er^2 = Kq
q = Er^2/K
q = 4.70 N/C * (3.20 m)^2/9.0 * 10^9
q = 5.35 * 10^-9 C
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A bullet is fired horizontally with an initial velocity of 900 m/s at a target located 150 m from the rifle.
a) How much time is required for the bullet to reach the target?
b) Using the approximate value of g = 10 m/s^2, how far does the bullet fall in this time?
If you could show work, that'd be greatly appreciated :) I know the answers, but I'm not sure how they're worked.
Answer:
S = Vx t = 900 t
t = 150 / 900 = 1/6 sec
If the bullet is fired horizontally it will travel 900 m in .167 sec
H = 1/2 g t^2 = 1/2 * 10 * (1/6)^2 = .139 m distance bullet will fall
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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A person has a reasonable chance of surviving an automobile crash if the deceleration is no more than 30 "g's."Calculate the magnitude of the force on a 89-kg person accelerating at this rate.
The magnitude of the force on the 89 kg person who is decelerating at 30 m / s² is 272.44 N
According to Newton's second law of motion,
F = m a
m = W / g
F = Force
m = Mass
a = Acceleration
W = Weight
g = acceleration due to gravity
a = 30 m / s²
W = 89 kg
F = 89 * 30 / 9.8
F = 272.44 N
According to Newton's second law of motion, Acceleration of an object is dependent upon the mass of the object and the net force acting on it.
Therefore, the magnitude of the force on the 89 kg person who is decelerating at 30 m / s² is 272.44 N
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The internet in countries like North Korea Saudi Arabia and China is
Answer:
Explanation:
The correct answer will be that the internet in north korea, Saudi Arabia and china is controlled by the government.
As in these countries according to the constitution of these countries there is a very much restriction on the civilians even for the internet usage. So the internet usage is controlled by the government in these countries.
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reach a top speed of 114 km/h (71 mi/h). While chasing its prey in a short sprint, a cheetah starts from rest and runs 47 m in a straight line, reaching a final speed of 78 km/h.
(a) Determine the cheetah's average acceleration during the short sprint. m/s²
(b) Find its displacement at t = 3.1 s. (Assume the cheetah maintains a constant acceleration throughout the sprint.)
(a) The cheetah's average acceleration during the short sprint is 5.67 m/s²
(b) The displacement of the cheetah after the given time is 94.42 m.
Average acceleration of the cheetah
The average acceleration of the cheetah is calculated as follows;
v² = u² + 2as
where;
u is initial velocity = 78 km/h = 21.67 m/s
v is the final velocity = 114 km/h = 31.67 m/s
31.67² = 21.67² + 2(47)a
31.67² = 21.67² + (94)a
94a = (31.67² - 21.67²)
a = (31.67² - 21.67²)/94
a = 5.67 m/s²
Displacement of the cheetahs = ut + ¹/₂at²
s = (21.67 x 3.1) + ¹/₂(5.67)(3.1²)
s = 94.42 m
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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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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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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)
What safety features are commonly found in the car’s interior? (2 pts)
Answer: Airbag
Explanation:
Provides safety to passengers during a collision.
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 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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Select the best answer for the question.
4. The legal right given to a creator of a work to profit from it is known as
OA. artistic license.
OB. digital permission.
C. plagiarism.
OD. copyright.
Mark for review (Will be highlighted on the review page)
<< Previous Question
Next estion >>
1
Answer:
Explanation:
The correct option will be the option (d) that is copyright.
The legal right given to a creator for a work to earn profit from it is known as copyright. That works can be about books, music, painting, sculptures, and films, any database programs, advertisements, new technology, maps etc. if any person doesn’t the follow the protocols of this copyright rule then he/she will be punished. For that he/she might have to pay some money for stealing the creator’s work.
So, the correct option will be the copyright.
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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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(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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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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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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