A boat crossing a 153.0 m wide river is directed so that it will cross the river as quickly as possible. The boat has a speed of 5.10 m/s in still water and the river flows uniformly at 3.70 m/s. Calculate the total distance the boat will travel to reach the opposite shore.
Answers
We have the relation
[tex]\vec v_{B \mid E} = \vec v_{B \mid R} + \vec v_{R \mid E}[/tex]
where [tex]v_{A \mid B}[/tex] denotes the velocity of a body A relative to another body B; here I use B for boat, E for Earth, and R for river.
We're given speeds
[tex]v_{B \mid R} = 5.10 \dfrac{\rm m}{\rm s}[/tex]
[tex]v_{R \mid E} = 3.70 \dfrac{\rm m}{\rm s}[/tex]
Let's assume the river flows South-to-North, so that
[tex]\vec v_{R \mid E} = v_{R \mid E} \, \vec\jmath[/tex]
and let [tex]-90^\circ < \theta < 90^\circ[/tex] be the angle made by the boat relative to East (i.e. -90° corresponds to due South, 0° to due East, and +90° to due North), so that
[tex]\vec v_{B \mid R} = v_{B \mid R} \left(\cos(\theta) \,\vec\imath + \sin(\theta) \, \vec\jmath\right)[/tex]
Then the velocity of the boat relative to the Earth is
[tex]\vec v_{B\mid E} = v_{B \mid R} \cos(\theta) \, \vec\imath + \left(v_{B \mid R} \sin(\theta) + v_{R \mid E}\right) \,\vec\jmath[/tex]
The crossing is 153.0 m wide, so that for some time [tex]t[/tex] we have
[tex]153.0\,\mathrm m = v_{B\mid R} \cos(\theta) t \implies t = \dfrac{153.0\,\rm m}{\left(5.10\frac{\rm m}{\rm s}\right) \cos(\theta)} = 30.0 \sec(\theta) \, \mathrm s[/tex]
which is minimized when [tex]\theta=0^\circ[/tex] so the crossing takes the minimum 30.0 s when the boat is pointing due East.
It follows that
[tex]\vec v_{B \mid E} = v_{B \mid R} \,\vec\imath + \vec v_{R \mid E} \,\vec\jmath \\\\ \implies v_{B \mid E} = \sqrt{\left(5.10\dfrac{\rm m}{\rm s}\right)^2 + \left(3.70\dfrac{\rm m}{\rm s}\right)^2} \approx 6.30 \dfrac{\rm m}{\rm s}[/tex]
The boat's position [tex]\vec x[/tex] at time [tex]t[/tex] is
[tex]\vec x = \vec v_{B\mid E} t[/tex]
so that after 30.0 s, the boat's final position on the other side of the river is
[tex]\vec x(30.0\,\mathrm s) = (153\,\mathrm m) \,\vec\imath + (111\,\mathrm m)\,\vec\jmath[/tex]
and the boat would have traveled a total distance of
[tex]\|\vec x(30.0\,\mathrm s)\| = \sqrt{(153\,\mathrm m)^2 + (111\,\mathrm m)^2} \approx \boxed{189\,\mathrm m}[/tex]
Related Questions
Transverse waves are to radio waves as longitudinal waves are to:
1. light waves
2. microwaves
3. ultraviolet waves
4. sound waves
URGENT!!!!
Answers
4
D
4. Sound Waves.
Explanation
The first three options are electromagnetic radiations (including radio waves), which are transverse waves. Sound waves is a longitudinal wave as it oscillates in the direction by which the wave propagates.
An electron and a proton have charges of an equal magnitude but opposite sign of 1.60 10-19 C. If the electron and proton in a hydrogen atom are separated by a distance of 2.00 10-11 m, what are the magnitude and direction of the electrostatic force exerted on the electron by the proton
Answers
The proton's electrostatic force exerted on the electron will be 3.5×10¹² N.
What is the electrostatic force?It is a force imposed by one charge on another as a result of the field.
The electrostatic force produced by one line charge on another line charge separated by r is determined by the charge potency of each charge as well as the separation distance between them.
The electrostatic force is found as:
[tex]\rm F= \frac{Kq_1q_2}{R^2} \\\\ F= \frac{9 \times 10^ 9 \times 1.6 \times 10^{-19} \times -1.6 \times 10^{-19} }{(2.00\times 10^{-11})^2} \\\\\ F= 3.5 \times 10^{12} \ N[/tex]
Hence, the proton's electrostatic force exerted on the electron will be 3.5×10¹² N.
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The current through a 12 Ω resistor in an electric circuit is 1.5 A. Calculate the potential difference across the resistor.
Answers
Hello!
We can use Ohm's Law to solve for the potential difference across a resistor given the current and resistance:
[tex]V = iR[/tex]
V = Potential Difference (? V)
i = Current (1.5 A)
R = Resistance (12 Ω)
Plug in the known values and solve.
[tex]V = (1.5)(12) = \boxed{18 V}[/tex]
Our galaxy, the milky way, contains approximately 4.0x1011 starts with an average mass of 2.0x1030kg each. how far away is the milky way from our nearest neighbor, the andromeda galaxy, if andromeda contains roughly the same number of stars and attracts the milky way with a gravitational force of 2.4x1030n?
Answers
By applying the law of universal gravitation, the distance between the milky way and the andromeda galaxy is equal to 4.2 × 10¹¹ meters.
Given the following data:
Mass A, m = 4.0 × 10¹¹ kg.Mass B, M = 2.0 × 10³⁰ kg.Gravitational force, F = 2.4 × 10³⁰ Newton.Scientific data:
Gravitational constant = 6.67 × 10⁻¹¹ m/kg²
How to calculate the distance?In order to determine the distance between the milky way and the andromeda galaxy, we would apply the law of universal gravitation.
According to the law of universal gravitation, the distance between two astronomical bodies can be calculated by using this formula:
[tex]d = \sqrt{\frac{GmM}{F} }[/tex]
Substituting the parameters into the formula, we have;
[tex]d = \sqrt{\frac{6.67 \times 10^{-11} \times 2.0 \times 10^{30} \times 4.0 \times 10^{11}}{2.4 \times 10^{30}} }[/tex]
Distance, d = 4.2 × 10¹¹ meters.
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Help meeee is for tomorrow, plssss!!!
2) For the association of resistors below:
a) The equivalent resistor between A and B.
b) The total electric current that runs through the circuit, knowing that the electrical voltage between terminals A and B is valid 21 V(volts).
c) The value of the electric current passing through the resistor of 1.0 Ohm.
d) The power dissipated through the 8.0 Ohm resistor.
Answers
(a) The equivalent resistance of the circuit is 0.52 ohms.
(b) The total electric current that runs through the circuit is 40.38 A.
(c) The value of the electric current passing through the resistor of 1.0 Ohm is 21 A.
(d) The power dissipated through the 8.0 Ohm resistor is 55.13 W.
Equivalent resistance of the circuitThe equivalent resistance of the circuit is calculated as follows;
1/R = 1/(1 + 1) + 1/(2 + 2 + 2) + 1/(6) + 1/(2) + 1/8 + 1/8 + 1/6 + 1/6
1/R = 1/2 + 1/6 + 1/6 + 1/2 + 1/8 + 1/8 + 1/6 + 1/6
1/R = 1 + 2/3 + 1/4
1/R = 23/12
R = 12/23
R = 0.52 ohms
Total current through the circuitV = IR
I = V/R
I = 21/0.52
I = 40.38 A
Current through 1 ohm resistorV = IR
I = V/R
I = 21/1
I = 21 A
Power dissipated through 8 ohm resistorP = V²/R
P = (21)²/8
P = 55.13 W
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During the course of a concert, the temperature of a pipe organ gradually increases. As a result, the frequency of the sound from each pipe will ______ throughout the concert.
Answers
Sean, who has a mass of 65-kg, is out roller blading with friends at a speed of 3 m/s. Not realizing he accidentally let the dog out as he was leaving, Sean finds his 12-kg pup at rest in the middle of the street. Sean gracefully scoops the dog up as he skates down the road and proceeds to carry the pup home. Calculate their final velocity.
Velocity: _ m/s
Answers
Answer:
2.53m/s
Explanation:
Initial momentum in a system= Final momentum in a system
65kg*3m/s+12kg*0m/s=(65kg+12kg)*v
195kgm/s=77kg*v
v=2.53m/s
A 20.00 kg lead sphere is hanging from a hook by a thin, massless wire 2.80 m long and is free to swing in a complete circle. Treat the sphere as a point mass. Suddenly it is struck horizontally by a 5.00 kg steel dart that embeds itself in the lead sphere. What must be the minimum initial speed of the dart so that the combination makes a complete circular loop after the collision
Answers
The minimum initial speed of the dart so that the combination makes a complete circular loop after the collision is 58.5 m/s.
Minimum speed for the object not fall out of the circle
The minimum speed if given by tension in the wire;
T + mg = ma
T + mg = m(v²)/R
tension must be zero for the object not fall
0 + mg = mv²/R
v = √(Rg)
Final speed of the two mass after collisionUse the principle of conservation of energy
K.Ef = K.Ei + P.E
¹/₂mvf² = ¹/₂mv² + mg(2R)
¹/₂vf² = ¹/₂v² + g(2R)
¹/₂vf² = ¹/₂(Rg) + g(2R)
vf² = Rg + 4Rg
vf² = 5Rg
vf = √(5Rg)
vf = √(5 x 2.8 x 9.8)
vf = 11.7 m/s
Initial speed of the dartApply principle of conservation of linear momentum for inelastic collision;
5v = vf(20 + 5)
5v = 11.7(25)
5v = 292.5
v = 58.5 m/s
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Which of the following is a good radiator of heat option is (a) a shiny silvered surface option (b) a dull black surface option (c) a white surface option (d) a green coloured surface
Answers
Answer:
option b
Step by step explanation:
a dull black surface is a good radiator of heat
Answer:
option b is the answer
A child jumps from a moving sled with a speed of 2.2 m/s and in the
direction opposite the sled's motion. The sled continues to move in the forward direction, but with a new speed of 5.5 m/s. If the child has a mass of 38 kg and the sled has a mass 68 kg, what is the initial velocity of the sled?
Answers
The initial velocity of the sled will be 7.34 m/sec. V is the initial velocity of the sled.
What is the law of conservation of momentum?According to the law of conservation of momentum, the momentum of the body before the collision is always equal to the momentum of the body after the collision.
The given data in the problem is;
(m₁) mass of child = 38 kg
(u₁) is the initial velocity child = 2.2 m/s
(m₂) is the mass of sled = 68 kg
(u₂) is the initial velocity of sled = ?
(v) is the velocity after collision = 5.5 m/s
According to the law of conservation of momentum;
Momentum before collision =Momentum after collision
[tex]\rm m_1u_1 + m_2u_2 = v(m_1 + m_2)\\\\(38 \times 2.2) + (68 \times V) = 5.5 \times (38+68) \\\\ 83.6 + 68V = 5.5 \times 106 \\\\ 83.6 + 68V =583 \\\\ \rm 68\ V= 583 -83.6 \\\\ \rm 68 \ V= 499.4\\\\ V= 7.34 \ m/sec[/tex]
Hence,the initial velocity of the sled will be 7.34 m/sec.
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how long would it take for a resultant upward force of hundred Newton to increase the speed of 50 kg object from hundred metre per second to 150 metre per second?
Answers
To answer this question, two equations are needed.
F = m * a (force = mass * accelaration)
Vf =Vi + (a * t) (final velocity = initial velocity + (accelaration * time)
Knowing that the force is 100 N and the mass is 50 kg we can use the first equation to solve for the acceleration which would be 2 m/s^2.
Plugging in all we know to the second equation we get:
150 m/s = 100 m/s + (2 m/s^2 * t)
This gives us t = 25 seconds
Can someone tell me what to tick and why for sentences 3 and 5 please
I will give brainliest to whoever answers correct
Answers
Measured in joules - Thermal energy
Measured with a thermometer - Temperature
Does not depend on how much material there is - Thermal energy
Measured in degrees Celsius - Temperature
Increases if you heat something for longer - Thermal energy
Which energy transformation occurs when an electrolytic cell is in operation.
Answers
Answer:
An electrolytic cell converts electrical energy into chemical energy.
Explanation:
A cylinder 15.0 cm in diameter rotates at 1000 rpm. (a) what is its angular velocity in rad/s? (b) what is the tangential velocity of a point on the rim of the cylinder?
Answers
Answer:
(a) Approximately [tex]105\; {\rm rad \cdot s^{-1}}[/tex].
(b) Approximately [tex]15.7\; {\rm m \cdot s^{-1}}[/tex], assuming that this cylinder is rotating along the axis that goes through the center.
Explanation:
The unit [tex]{\rm rpm}[/tex] stands for "revolutions per minute", where each revolution is [tex]2\, \pi[/tex] radians.
With an angular velocity of [tex]1000\; {\rm rpm}[/tex], this cylinder would turn [tex]1000\times 2\, \pi = 2000\, \pi[/tex] radians every minute ([tex]60\; {\rm s}[/tex]). Thus, the angular velocity of this cylinder would be:
[tex]\begin{aligned} \omega &= \frac{2000\, \pi\; {\rm rad}}{60\; {\rm s}} \\ &\approx 104.720\; {\rm rad \cdot s^{-1}}\end{aligned}[/tex].
A point at the rim of this cylinder would be at a distance of [tex]r = 15.0\; {\rm cm} = 0.150\; {\rm m}[/tex] from the axis of revolution of this cylinder. If the angular velocity of this cylinder is [tex]\omega[/tex], the tangential velocity of this point would be:
[tex]\begin{aligned} v&= \omega\, r \\ &= \frac{2000\, \pi}{60\; {\rm s}} \times 0.150\; {\rm m} \\ &\approx 15.7 \; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
A model train running on an inclined track is part of a closed system that has
316 J of mechanical energy. If the kinetic energy of the train decreases from
314 J to 250 J, what happens to the gravitational potential energy of the
system?
A. It decreases from 66 J to 2 J.
B. It decreases from 316 J to 314 J.
SMIT
OC. It increases from 2 J to 66 J.
D. It increases from 316 J-to 564 J.
Answers
If the kinetic energy of the train decreases from 314 J to 250 J, the gravitational potential energy of the system It increases from 2 J to 66 J.
What is conservation of mechanical energy?The principle of conservation of mechanical energy states that the total mechanical energy of a system is always constant. This means that the sum of the potential and the kinetic energy does not change.
Thus, if the kinetic energy of the train decreases from 314 J to 250 J, the gravitational potential energy of the system It increases from 2 J to 66 J.
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At 6: 00 am, a motorbike set off from town A to town B at a speed of 40km/h. At the same time, a car set off from town B to town A at a speed of 60km/h. What time did they meet
Answers
Answer:
One would need to know how far apart the towns are:
T = SA / 40 time it takes for first cyclist to travel S1
T = SB / 60 time it takes for cyclist B to travel distance S2
SA + SB = S the distance between the towns
SB = 60 / 40 SA = 1.5 SA
SA + 1.5 SA = S
S = 2.5 SA where cyclist travels distance SA
The time will depend on the separation of the towns.
Sound travels at a rate of 340 m/s in all directions through air. Matt rings a very loud bell at one location, and Steve hears it some time later at his location 450 meters to the south. How long did it take the sound to travel from the bell to Steve's location?
Answers
Answer:
110 m/s
Explanation:
because if you subtract 450 from 340 you get 110
The centers of two 350 kg spheres are separated by 2.00 m. what is the gravitational force between them?
Answers
please help with this i am not good with this
Answers
Answer:
Ball 3 (tennis ball)
Explanation:
Formula we are using :
acceleration = Force / mass
=============================================================
Ball 1 :
⇒ acceleration = 15 N / 0.5 kg
⇒ acceleration = 30 m/s²
===========================================================
Ball 2 :
⇒ acceleration = 15 N / 4.5 kg
⇒ acceleration = 30/9 m/s²
⇒ acceleration = 10/3 m/s²
⇒ acceleration = 3.33 m/s²
===========================================================
Ball 3 :
⇒ acceleration = 15 N/ 0.05 kg
⇒ acceleration = 300 m/s²
============================================================
On comparing, we see that Ball 3 (tennis ball) has the greatest acceleration.
when the formula m*g=F-Fg is used?
Answers
The formula (ma = F - Fg) is used to determine the net upward force acting on a body.
What is net upward force acting on a body?The net upward force acting on a body is the resultant or sum of all the upward forces acting on a body at a given time.
ma = F - Fg
where;
F is the applied forceFg is the force of gravityma is the resultant forceThus, the formula (ma = F - Fg) is used to determine the net upward force acting on a body.
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how many cubic meters of habitable space was available in skylab?
A 1,000
B 263
C 5,263
D 10,000
Answers
361 cubic meters of habitable space was available in the skylab. None of the given options are correct.
Who launched skylab?NASA launched the first American space station, called Skylab.
The fuel tank of the Saturn SIV-B rocket stage served as the Skylab's residential quarters.
Skylab's livable capacity was large in comparison to the spacecraft that American astronauts had previously used 361 cubic meters.
Skylab offered 361 cubic meters of livable area.
Hence, none of the given options is correct.
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A rock is dropped from a garage roof from rest. the roof is 6.0 m from the ground. determine the velocity of the rock as it hits the ground.
Answers
From rest, a rock is dropped from a garage roof. The roof is 6.0 meters above ground level. The rock will reach the earth at a speed of 10.849 meters per second.
What is velocity?The change of displacement with respect to time is defined as the velocity. Velocity is a vector quantity.
it is a time-based component. Velocity at any angle is resolved to get its component of x and y-direction.
Given data:
V(Final velocity)=? (m/sec)
h(height)= 6.0 m
u(Initial velocity)=0 m/sec
g(gravitational acceleration)=9.81 m/s²
Newton's third equation of motion:
[tex]\rm v_y^2 = u_y^2+ 2gh \\\\\rm v_y^2 = 0+ 2gh\\\\\ v_y= \sqrt{2\times 9.81 \ (m/s^2)\times 6.0 (m)} \\\\ v_y=10.849 \ m/sec[/tex]
Hence, the velocity of the rock as it hits the ground will be 10.849 m/sec.
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An electromagnetic wave has a wavelength of 10 nm. Calculate its frequency and identify to which part of the electromagnetic spectrum the wave belongs.
Answers
The frequency of an electromagnetic wave with wavelength of 10nm will be 3 × 10∧7 Hz and would belong to the X-ray or ultraviolet part of the electromagnetic spectrum due to its wavelength
What is frequency?
Frequency is defined as the number of oscillations of a wave per unit time and is measured in hertz(Hz).
It is also inversely proportional to the wavelength.
How to calculate the frequency
The frequency of an electromagnetic wave can be calculated using the formula;
frequency = velocity of light divided by the wavelength
f = v ÷ λ
Note that the velocity of light = 3 × 10 ∧8 m/s
Wavelength = 10nm
Frequency, f = 3 × 10∧8 ÷ 10 = 3 × 10∧7 Hz
Hence, the frequency of an electromagnetic wave with wavelength of 10nm will be 3 × 10∧7 Hz and would belong to the X-ray or ultraviolet part of the electromagnetic spectrum due to its wavelength.
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The chart show the masses and velocities of two colliding objects that stick together after a collision.
According to the law of conservation of momentum, what is the momentum of the object after the collision?
4,500 g · m/s
1,750 g · m/s
1,500 kg · m/s
3,000 kg · m/s
Answers
The momentum of the object after the collision is 1500 kg. m/s.
What is conservation of momentum principle?When two bodies of different masses move together each other and have head on collision, they travel to same or different direction after collision.
The external force is not acting here, so the initial momentum is equal to the final momentum. In inelastic collision, after the collision, the two objects are stick together and final velocity is the common velocity for both the bodies.
Given is the chart show the masses and velocities of two colliding objects that stick together after a collision.
Object Mass (kg) Velocity (m/s)
A 200 15
B 150 - 10
Using the conservation of momentum principle, we have
m₁u₁ +m₂u₂ =(m₁ +m₂) v = Pf
Substitute the values, then the momentum after collision will be
200x15 +150x(-10) =Pf
Pf = 1500 kg. m/s
Thus, the momentum after collision is 1500 kg. m/s.
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A 500 N weight is hung at the middle of a rope attached to two buildings at the same level. If the breaks in the tension exceed 1800 N, what is the minimum angle the rope can make with the horizontal?
Answers
Not sure what you mean by "breaks in the tension" but I suspect you mean the rope will come apart if the tension in the rope exceeds 1800 N.
In the free body diagram for the 500 N weight, we have a figure Y with the net force equations
• horizontal net force:
∑ F[hor] = T₁ cos(θ) - T₂ cos(θ) = 0
• vertical net force:
∑ F[ver] = T₁ sin(θ) + T₂ sin(θ) - 500 N = 0
From the first equation, it follows that T₁ = T₂, so I'll denote their magnitude by T alone. From the second equation, we have
2 T sin(θ) = 500 N
and if the maximum permissible tension is T = 1800 N, it follows that
sin(θ) = (500 N) / (3600 N) ⇒ θ = arcsin(5/36) ≈ 7.9°
is the smallest angle the rope can make with the horizontal.
A chemical reaction is the only way to separate a(n)
Answers
Answer:
pure substance
Explanation:
yw
According to Ohm’s law, which is stated as I = V ÷ R, which two sentences are true?
If the current increases, then the resistance increases. Assume voltage is constant.
If the resistance decreases, then the current increases. Assume voltage is constant.
If the voltage increases, then the resistance decreases. Assume current is constant.
If the voltage increases, then the current increases. Assume resistance is constant.
If the voltage increases, then the current decreases. Assume resistance is constant.
Answers
Answer:
2nd and 4th statements.
Explanation
If voltage is constant ( k ) and I = V / R,
Then I is inversely proportional to R so if I increases R decreases and vice versa, according to that the second statement is correct not the first.
if current is constant, then v is directly proportional to R and vice versa..the 3rd statement is wrong
if resistance is constant v is directly proportional to I, then only the 4th is correct not the 5th
10. In Freudian theory, which one of the following is an example of a Thanatos instinct, which includes aggression, trauma, and risky behaviors?
A. going to school.
B. seeking nourishment.
C. joining a basketball club.
D. substance abuse.
Answers
In Freudian theory, substance abuse is one of the following an example of a Thanatos instinct, It includes aggression, trauma, and risky behaviors, Therefore the correct answer is option D
What is the Freudian theory?The psychoanalytic approach to adult personality development is built on the theories of Sigmund Freud. His beliefs addressed four topics: level of consciousness, personality structure, and stages of psychosexual development. These personality qualities interact to create anxiety, which needs to be controlled via a range of defense mechanisms. These strategies mask the true, anxiety-related causes of one's conduct.
Freud's theories also have limited applicability to the fields of gerontology and geriatric medicine because they postulate that personality development related to his stages of psychosexual development essentially ends in adolescence.
Thus, Substance abuse is one of the Thanatos instincts, which also include aggression, trauma, and risky behavior, according to Freudian theory. Option D is the correct answer.
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A scientist tested wellwarm to see how well it insulated a beaker of hot water. she tested wellwarm and three other materials. what was the dependant variable that the scientist measured during the investigation?
Answers
Answer:
the dependent variable is the material
Explanation:
because we change the material each time to test which is the best insulator.
this came up in my test today, so i can assure you it is correct!
The prop blades of an airplane spin with a linear velocity of 875 m/s and have a centripetal acceleration on the farthest edge of 180,000 m/s^2 the radius of the prop blades?
Answers
The radius of the prop blade of an airplane is determined as 4.25 m.
Radius of the prop blade
The radius of the prop blade of an airplane is calculated as follows;
a = v²/r
where;
v is the linear speedr is the radius of the prop bladea is the centripetal accelerationr = v²/a
r = (875²)/(180,000)
r = 4.25 m
Thus, the radius of the prop blade of an airplane is determined as 4.25 m.
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