An athlete needs to get across a river. She must reach from point A on one bank to point B, which is directly across from point A on the opposite bank. If she wishes to minimize the total time T it would take to do so, at what angle upstreams (measured from the line AB) should she swim? Let her swimming/rowing speed relative to the water be 2.0 mi/h, and her running speed along the bank be 5 mi/h. The river flows downstream at 1.5 mi/h. (The rule of the competition stipulates that the athletes must swim first from point A, then run to reach point B.)
Answers
Answer:
θ = 90°
Explanation:
Speed at which she can swim in stationary water; v_m = 2 mi/h
Speed at which the river is flowing downstream; v_r = 1.5 mi/h
This can be illustrated in a form of triangle as attached. Where θ is the angle to the x-axis.
With respect to the bank of the river, the total speed of the girl is;
V_R = v_r + v_m
Now the horizontal component is;
V_R = v_r + v_m(cos θ)
While the vertical component is;
V_R = v_m(sin θ)
Now, the total time taken to get across the river is;
T = width of river/vertical component of total speed
Let's denote width of river as d.
Thus;
T = d/(v_m(sin θ))
Now, we are told she wishes o minimize the total time(T) .
Since the width(d) of the river is constant, and v_m is fixed, then it means the only variable we have is the angle θ.
Now, for the total time to be minimized, the denominator has to be at maximum.
Since angle θ is the only one that is variable, we have to find the value of angle θ that will make sin θ to be at a maximum value.
Now, for sin θ to be maximum, it means it has to be equal to 1.
Thus, θ = sin^(-1) 1
θ = 90°
Related Questions
what is true about a horizontally launched projectile?
Answers
Answer:
it has lateral momentum
Explanation:
it explains itself
a girl on a bridge throws a rock straight down at -12.5 m/s. it hits the ground 38.4 m below. How much time did it take?
Answers
[tex]\\ \rm\rightarrowtail s=ut+\dfrac{1}{2}gt^2[/tex]
[tex]\\ \rm\rightarrowtail 38.4=12.5t+4.9t^2[/tex]
On solving further we get
t=1.8sA girl on a bridge throws a rock straight down at -12.5 m/s.the time required to hit the ground 38.4 m below is 4.35 s.
Given:
Speed, u = -12.5 m/s
Distance, d = 38.4 m/s
There are three equations of motion present. For the given question, we will use the second equation of motion.
The second equation of motion helps in the determination of velocity, time, and distance. For the given question, we have initial velocity, and distance, to find time we can use the second equation of motion.
From the second equation of motion:
[tex]s = ut + 1/2 at^2\\38.4 = -12.5t - 9.8/2* t^2\\\4.9t^2 - 12.5 t -38.4 = 0[/tex]
Solving the equation, the required time is:
[tex]t = 4.35 s[/tex]
Hence, the time required to hit the ground 38.4 m below is 4.35 s.
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2
In 1987, the fastest auto race in the United States was the Busch Clash in Daytona, Florida. That year, the
winner's average speed was about 318 km/h. Suppose the kinetic energy of the winning car was 3.80 MJ. What
was the mass of the car and its driver?
Answers
Since the winner's average speed was about 318 km/h and the kinetic energy of the winning car was 3.80 MJ. So, the mass of the car and its driver is 974 kg.
Kinetic energyThe kinetic energy of the car is given by K = 1/2mv² where
m = mass of car and driver and v = average speed of car = 318 km/h = 318 × 1000 m/3600 s = 88.33 m/sMass of the car and driverMaking m subject of the formula, we have
m = 2K/v²
Since K = 3.80 MJ = 3.80 × 10⁶ J, substituting the values of the variables into the equation, we have
m = 2K/v²
m = 2 × 3.80 × 10⁶ J/(88.33 m/s)²
m = 7.6 × 10⁶ J ÷ (7802.78 m²/s²)
m = 7600000 J ÷ 7802.78 m²/s²
m = 974.01 kg
m ≅ 974 kg
So, the mass of the car and its driver is 974 kg
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Sand and salt are poured into a single beaker. The result is a mixture because_____?
Answers
Answer:
Sand and salt are poured into a single beaker. The result is a mixture because they can be separated by simple and easy physical means.
Explanation:
Mixture : Properties :
They are put in a indefinite proportion.They are physically mixed with each other.They can be separated by physical and easily methodsConstituents retain their own propertiesNow let us see these in the perspective of the question :
We could have put more of salt and less of sand, still it would not have become a compound. We had poured it into a single beaker with some physical means.We can use sedimentation and evaporation to separate them. After separating them, the will retain their own properties, it is not that the salt will become bitter or the sand will start not allowing the water to flow through it.These are some few reasons why these getting mixed, becomes a mixture, and we can choose any one point of the properties of mixture and give the answer.
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A large toy car has a mass of 15 Kg and is pushed horizontally with a force of 2 N. Assume friction is so small it can be ignored. What is the acceleration?
Answers
Answer:
0.133 m/s²
Explanation:
F=ma
F is force
m is mass
a is acceleration
F=ma
2=15.a
a=2/15
a=0.133 m/s²
Amanda has started running as her primary form of exercise, but she's getting bored with it and finds excuses to procrastinate. It's also getting really hot outside now that it's summer, and Amanda's skin is sensitive to the sun. She has a significant budget available to help her fix the problem but is unsure how to spend the money.
What might be the most appropriate purchase for Amanda?
ANSWER please ⬆️⬆️⬆️ correctly! GIVING OUT BRAINLY STARS!!!
Answers
Answer:
: An app thr features menu planning with healthy recipes and pairs with a calorie tracking tool
Rihanna can go from 0-60 miles per hour in 3.5 seconds. Calculate the acceleration.
Please show ALL work and CIRCLE your answer.
Answers
Answer:
7.66 m/s²
Explanation:
The following data were obtained from the question:
Initial velocity (u) = 0 mph
Final velocity (v) = 60 mph
Time (t) = 3.5 s
Acceleration (a) =.?
Next, we shall convert mile per hour (mph) to metre per second (m/s). This can be obtained as follow:
Recall:
1 mph = 0.447 m/s
Initial velocity (u) = 0 mph
Initial velocity (u) = 0 × 0.447 = 0 m/s
Final velocity (v) = 60 mph
Final velocity (v) = 60 × 0.447 = 26.82 m/s.
Finally, we shall determine the acceleration of Rihanna as follow:
Initial velocity (u) = 0 m/s
Final velocity (v) = 26.82 m/s.
Time (t) = 3.5 s
Acceleration (a) =.?
a = (v – u) /t
a = (26.82 – 0) / 3.5
a = 26.82 / 3.5
a = 7.66 m/s²
Thus, the acceleration of Rihanna is 7.66 m/s²
1. You set the thermostat in your house to 70 degrees so that when it goes above that temperature the air conditioner will turn on. What is the feedback of this system? 2. You set the thermostat in your house to 70 degrees so that when it goes above that temperature the air conditioner will turn on. What is the input of this system?
PLEASE HELP
Answers
Answer:
Negative Feedback...... Temperature
Explanation:
as the Temperature increase more than the set point the air conditioner turn on to lower the temperature so that means it is Negative feedback because it is not INHANCING the temperature
Input should be Temperature or Heat because AC turns on when the temperature is getting above 70 degrees
NOW WHERE IS MY BRAINLIESTTTT
Which of the following statements about charging objects is FALSE. Select one: If an object gains electrons it becomes positively charged. If an object gains electrons it becomes negatively charged. Charges cannot travel in an insulator. Charges can travel in a conductor.
Answers
Answer:
If an object gains electrons it becomes positively charged.
Explanation:
Electrons negatively charge.
The Earth rotates once every day. What is the velocity of a person on its surface, if the radius of Earth is 6 million meters
Answers
Answer:
v = ω R
number of seconds in 24 hrs = 24 * 3600 = 86400 s / da = T (period)
f = 1 / T
ω = 2 Π f = 2 Π / T = 2 Π / 86400
v = 2 Π / 8.64E4 * 6.0E6 = 436 m / s
Check:
S = 2 Π * 6.0E6 = 3.77E7 m/da
S / T = 3.77E7 m/da / 8.64E4 s/da = 436 m / s
differentiate kinetic energy from potential energy
Answers
The main difference between potential and kinetic energy is that one is the energy of what can be and one is the energy of what is. In other words, potential energy is stationary, with stored energy to be released; kinetic energy is energy in motion, actively using energy for movement.
Hope it helps you! :)
Answer:
Potential energy is the energy that happens before kinetic energy, it might be slow and preparing for the kinetic energy act. Kinetic energy is the outcome of the potential energy. You can say a man climbing a hill with his bike is potential energy, and when he rides his bike down is kinetic energy
How can you strengthen the magnetic force of an electromagnet? (check all that apply)
(I'M TAKING TEST PLEASE HELP)
A. Increase the voltage of the battery attached to the electromagnet.
B. Increase the wire coils wrapped around the metal core.
C. Spread out the wire coils wrapped around the metal core.
D. Increase the number of batteries attached to the electromagnet.
Answers
1 wrapping the coil around a piece of iron (such as an iron nail)
2 adding more turns to the coil.
3 increasing the current flowing through the coil.
What variables do you think affect the strength of the force of gravity between two objects?.
Answers
Answer:
Mass and distance.
Explanation:
The force of gravity is proportional to the masses of the two objects and inversely proportional to the square of the distance between them.
QUESTION 4
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If a car is moving at 37 km/h for 42 min, what is the distance that the car has traveled. (Give your answer in terms of meters and round to
the nearest whole number.)
Answers
Answer:
s=25956m
Explanation:
first 37 km/h is 10.3 m/s
then 42 min is 2520s
finally s=vt => s=2520s*10.3m/s
s=25,956m
Answer:
25956
Explanation:
Convert 37km/h to m/s =10.3m/s
Where s=vt
S=10.3×2520
S=25,956
S=25,000
A transformer has 500 volts applied to the primary side and 10,000 volts are measured
on the secondary side. If 10mA is applied to the primary side. What is the anticipated
current on the secondary side? Is this a step-up or step down transformer?
Answers
Answer:
0.5 mA, step-up transformer
Explanation:
Power is constant
V * I = constant
500 V * 10 mA = 10,000 V * I
so I = 0.5 mA
From 500 V increases to 10,000 V, so it is a step-up transformer
A student is moving a magnet through a coil of wire. Which of these indicates the strength of the electric current in the coil?
Answers
Answer:
Can you help me with another question
Explanation:
The electric current in the coil depends on changes in the magnetic field of the magnet.
Electricity is generated when there is relative motion between a conductor and a magnetic field. As the magnet is being moved through the coil of wire, the magnetic flux around the conductor changes and current is induced on it.
Hence, the strength of the electric current in the coil is determined by changes in the magnetic field of the magnet.
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A skydiver has a mass of 80 kg. When she is at a height of 900 m, her GPE is
705,600 J. She is falling at a velocity of 32 m/s downward. What is her ME at this
point?
Answers
Answer:
11.25 J
Explanation:
GPE=wxh=80kg over 900m=11.25 J
what is lighting write its causes
Answers
Answer: lightning is the occurrence of a natural electrical discharge of very short duration and high voltage between a cloud and the ground or within a cloud, accompanied by a bright flash and typically also thunder.
the causes of lightning:
Lightning happens when the negative charges (electrons) in the bottom of the cloud are attracted to the positive charges (protons) in the ground.
In the early stages of development, air acts as an insulator between the positive and negative charges in the cloud and between the cloud and the ground. When the opposite charges build up enough, this insulating capacity of the air breaks down and there is a rapid discharge of electricity that we know as lightning.
5. Use the algebraic technique for adding vectors to find the total displacement of a person who walks the following three paths (displacements-on a flat field. First, she walks 25.0 m in a direction 49.00 north of east. Then she walks 23.0 m heading 15.00 north of east. Finally, she turns and walks 32.0 m in a direction 68.0° south of east.
Answers
Answer:
jjjjjjjjjjjjjjjj
Explanation:
A boulder of mass 4 kg rolls over a cliff and reaches the beach below with a velocity of 20 metres per second minus 1.
what is the kinetic energy of the boulder when it lands?
what is the potential energy on the cliff?
How high is the cliff??
Answers
Given:-
Mass of boulder = 10kg
Final Velocity = 15m/s
Acceleration due to gravity = +10m/s
To Find:-
The kinetic energy of the boulder as it lands
The potential energy of the boulder when it was at the top of the cliff
The height of the cliff
Formulae used:-
Kinetic energy = mv²/2
Potential energy = mgh
Now,
We will first find the Kinetic enrgy,
→ K. E = ½mv²
→ K. E = ½ × 10 × (15)²
→ K. E = 5 × 225
→ K. E =1125J
But we know that when the body starts moving the Potential enrgy of the body starts Converting into Kinetic enrgy. Before reaching to the last spot it has equal kinetic energy and Potential energy.
Therefore,
→ mgh = 1125J
The Potential enrgy of the boulder when it was on top is 1125J
Now,
→ mgh = 1125J
→ 10 × 10 × h = 1125J
→ 100h = 1125J
→ h = 1125/100
→ h = 11.25m
Hence, The Height of the Cliff is 11.25m
Thanks!
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Condition when an organ is impaired sickness
Answers
Answer:
As traditionally used, impairment refers to a problem with a structure or organ of the body; disability is a functional limitation with regard to a particular activity; and handicap refers to a disadvantage in filling a role in life relative to a peer group.
Explanation:
Hope this helps u
Crown me as brainliest:)
Where is the stigma located?
Answers
Answer:
At the tip of the pistil
Explanation:
Hope it helped!
WHO WANTS BRAINLY? PLEASE ANSWER THIS PHYSICS QUESTION!
force of 187 N acts on a 7.3 kg bowling ball for 0.40 s.
1. What is the change in momentum of the ball?
2. What is its change in velocity?
Answers
Change in momentum of the ball is 74.8 kg m/s
change in velocity of the ball is 0.25 m/s
What is change in momentum?
Change in momentum is the product of mass and change in velocity this is also equal to impusle which ia a product of force and time.
Change in momentum = m ( v - u ) = Impulse = f * t
m = mass
change in velocity = v - u
v = final velocity
u = initial velocity
f = force
t = time
Given:
f = 187 N
m = 7.3 kg
t = 0.40 s
!.
Change in momentum = impulse = f * t
Change in momentum = 187 * 0.40
Change in momentum = 74.8 kg m/s
2.
Change in momentum = m * ( v - u )
( v - u ) = change in momentum / m
( v - u ) = 187 / 7.3
( v - u ) = 10.25 m/s
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What occurs during stage one sleep
Answers
Answer:
Stage one of sleep, also known as the transitional phase, occurs when one finds themselves floating in and out of consciousness. During this NREM stage, you may be partially awake while your mind begins to drift off. This period of drowsiness eventually leads to a light sleep
Explanation:
i found it on google
29N, 60° +59N, 125° + 72N, 261°
Vectors
Answers
389wujh
which means it 240C
Which of the following best explains why engineers are constantly looking for innovative ways to investigate
and improve fluid power designs?
Changes in fluid power systems lead to increased sustainability, such as decreases in fuel costs and carbon emissions.
Changes in fluid power will reach all different types of applications beyond their current uses.
Changes in fluid power will not benefit efficiency ratings but will decrease the costs of products.
Changes are necessary as more designs and products are created and more power systems are required.
Answers
Answer:
Explanation:
What was the answer Im stuck on it rn...
Answer:
Changes in fluid power systems lead to increased sustainability, such as decreases in fuel costs and carbon emissions.
Explanation:
What is the final velocity of a drag racer that has constant acceleration and finishes a
1/4 mile race in 15 seconds?
Answers
Answer:
120 mph
Explanation:
Given:
Δx = 0.25 mi
v₀ = 0 mi/s
t = 15 s
Find: v
Δx = ½ (v + v₀) t
0.25 mi = ½ (v + 0 mi/s) (15 s)
v = 0.0333 mi/s
v = 120 mi/h
Solar energy can be directly converted to elec-trical energy by which of the following de-vices?
Answers
Answer: (c) solar cell
Explanation:
A solar cell takes solar energy directly from the sunlight and converts it into electrical energy
Which particles have more speed: Solid or Liquid? Why?
Answers
How does the organization know what their needs and expectations are ?
Answers
Answer:
When scientific knowledge changes overtime, it can be to anything at anytime. The Explosion in what we know about life form is important and change because we might have a plant we can’t touch or something like that. That is not the only thing that is important about how scientific knowledge change over time it is also the food pyramid. We know that especially The Explosion in What We Know About Life Forms, is because there might be like a new plant we can’t touch because say it is potions or something. According to the life forms article people are wondering if scientist have found all the living species on earth yet
Explanation: