A spacecraft on its way to Mars has small rocket engines mounted on its hull; one on its left surface and one on its back surface. At a certain time, both engines turn on. The one on the left gives the spacecraft an acceleration component in the x direction of
ax = 5.10 m/s2,
while the one on the back gives an acceleration component in the y direction of
ay = 7.30 m/s2.
The engines turn off after firing for 670 s, at which point the spacecraft has velocity components of
vx = 3670 m/s and vy = 4378 m/s.
What was the magnitude and the direction of the spacecraft's initial velocity before the engines were turned on? Express the magnitude as m/s and the direction as an angle measured counterclockwise from the +x axis.

magnitude m/s
direction ° counterclockwise from the +x-axis

Answers

Answer 1

Answer:

a)    v = 517.99 m / s,  b) θ = 296.3º

Explanation:

This is an exercise in kinematics, we are going to solve each axis independently

X axis

the acceleration is aₓ = 5.10 1 / S², they are on for t = 670 s and reaches a speed of vₓ=  3670 m / s, let's use the relation

           vₓ = v₀ₓ + aₓ t

           v₀ₓ = vₓ - aₓ t

           v₀ₓ = 3670 - 5.10 670

           v₀ₓ = 253 m / s

Y axis  

the acceleration is ay = 7.30 m / s², with a velocity of 4378 m / s after

t = 670 s

          v_y = v_{oy} + a_y t

          v_{oy} = v_y - a_y t

          v_oy} = 4378 - 7.30 670

          v_{oy}  = -513 m / s

to find the velocity modulus we use the Pythagorean theorem

          v = [tex]\sqrt{v_o_x^2 + v_o_y^2}[/tex]

          v = [tex]\sqrt{253^2 +513^2}[/tex]

          v = 517.99 m / s

to find the direction we use trigonometry

         tan θ ’= [tex]\frac{v_o_y}{v_o_x}[/tex]

         θ'= tan⁻¹  [tex]\frac{voy}{voy}[/tex]  

         θ'= tan⁻¹ (-513/253)

         tea '= -63.7

the negative sign indicates that it is below the ax axis, in the fourth quadrant

to give this angle from the positive side of the axis ax

          θ = 360 -   θ  

          θ = 360 - 63.7

          θ = 296.3º


Related Questions

g four small masses 0.2 kg each are connected by light rods 0.4m long to form a square.what is the moment of interia axis

Answers

Complete Question

Four small masses of 0.2 kg each are connected by light rods 0.4m long to form a square. What is the moment of inertia of this object for an axis through the middle of the square and parallel to two sides.

Answer:

[tex]I=0.032kgm^2[/tex]

Explanation:

From the question we are told that:

Mass[tex]m=0.2kg[/tex]

Length [tex]l=0.4m[/tex]

Generally the equation for Inertia is mathematically given by

 [tex]I=md^2[/tex]

 [tex]I=0.8*0.20(\frac{0.40}{2})^2[/tex]

 [tex]I=0.032kgm^2[/tex]

The electric potential ( relative to infinity ) due to a single point charge Q is 400 V at a point that is 0.6 m to the right of Q. The electric potential (relative to infinity) at a point that is 0.90 m to the left of 0 is:_____.
A. + 400 V.
B. -400 V.
C. + 200 V.

Answers

Answer:

The potential at a distance of 0.9 m is 266.67 V.

Explanation:

Charge = Q

Potential is 400 V at a distance 0.6 m .

Let the potential is V at a distance 0.9 m.

Use the formula of potential.

[tex]V = \frac{Kq}{r}\\\\\frac{V}{400}=\frac{0.6}{0.9}\\\\V = 266.67 V[/tex]

Momentum is defined as mass ___ velocity

Answers

Answer:
p=mv
Momentum = mass x velocity

momentum is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction.

I hope this helped :)
p=mv momentum is the answer

I need help with this problem can anybody help me please , it’s physics 2 course

Answers

Answer:

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Explanation:

The 2 capacitors in the middle are connected in parallel so simply add their capacitance together:

[tex]5.0\:\mu\text{F} + 8.0\:\mu\text{F} = 13.0\:\mu \text{F}[/tex]

Now we have 3 capacitors connected in series so their equivalent capacitance [tex]C_{eq}[/tex] is

[tex]\dfrac{1}{C_{eq}} = \dfrac{1}{10.0\:\mu \text{F}} + \dfrac{1}{13.0\:\mu \text{F}} + \dfrac{1}{9.0\:\ mu \text{F}} [/tex]

or

[tex]C_{eq} = 3.5\:\mu \text{F}[/tex]

A coin and feather are dropped in a moon. what will fall earlier on ground.give reasons.if they are dropped in the earth,which one will fall faster

Answers

Answer:

on the moon, they will fall at the timeon earth, the coin will fall faster to the ground

Explanation:

A coin and feather dropped in a moon experience the same acceleration due to gravity as small as 1.625 m/s², and because of the absence of air resistance both will fall at the same rate to the ground.

If the same coin and feather are dropped in the earth, they will experience the same acceleration due to gravity of 9.81 m/s² and because of the presence of air resistance, the heavier object (coin) will be pulled faster to the ground by gravity than the lighter object (feather).

Astronauts in space move a toolbox from its initial position ????????→=<15,14,−8>m to its final position ????????→=<17,14,−1>m. The two astronauts each push on the box with a constant force. Astronaut 1 exerts a force ????1→=<18,7,−12>???? and astronaut 2 exerts a force ????2→=<16,−10,16>????.

Required:
What is the total work performed on the toolbox?

Answers

If both forces are measured in Newtons, then the net force is

F = (18, 7, -12) N + (16, -10, 16) N = (34, -3, 4) N

The toolbox undergoes a displacement (i.e. change in position) in the direction of the vector

d = (17, 14, -1) m - (15, 14, -8) m = (2, 0, -9) m

The total work done by the astronauts on the toolbox is then

F • d = (34, -3, 4) N • (2, 0, -9) m = (68 + 0 - 36) N•m = 32 J

The work done by the two astronauts is equal to 96 J.

What is work done?

work done?Work done is defined as the product of force applied and the distance moved by the force.

Work done = Force × Distance

The forces applied = 18+16 N, 7+ -10 N, and -12 + 16N

Forces = 34 N, -3 N, and 4N

Distances = (17 - 15, 14 - 14, -1 - - 8) m

Distances = 2, 0, 7

Work done = 34 × 2 + -3 × 0 + 4 × 7

Work done = 96 J

Therefore, the work done by the two astronauts is equal to 96 J.

Learn more about work done at: https://brainly.com/question/25573309

#SPJ6

The equations for calculating both the electric force and the gravitational force are above. Their equations are very similar. What is an important difference between these two forces?

A The electrical force is measured in coulombs; the gravitational force is measured in newtons.

B The electrical force between two charged objects will always be weaker than the gravitational force between them.

C The gravitational force decreases with the square of the distance between the objects; the electrical force increases with the square of the distance between the objects.

D Electrical forces can be attractions or repulsions; gravitational forces can only be attractions.

Answers

A, B, and C are hilarious. D is correct.

Charges can be positive or negative, so a pair of charges can be alike or opposite. But so far, we've never seen a negative mass.

Gsjskebjwkksmndkkwksjdkdkskkskskkehdhjdj

Answers

Answer:

I DON'T UNDERSTAND

Explanation:

GUESS A MISUNDERSTANDING PLZ PUT A UNDERSTANDABLE QUESTION.

PLEASE HELP ME WITH THIS ONE QUESTION
The half-life of Barium-139 is 4.96 x 10^3 seconds. A sample contains 3.21 x 10^17 nuclei. How much of the sample is left after 1.98 x 10^4 seconds?

Answers

[tex]A=2.01×10^{16}\:\text{nuclei}[/tex]

Explanation:

Given:

[tex]\lambda = 4.96×10^3 s[/tex]

[tex]A_0 = 3.21x10^{17}[/tex] nuclei

t = 1.98×10^4 s

[tex]A=A_02^{-\frac{t}{\lambda}}[/tex]

[tex]A=(3.21×10^{17}\:\text{nuclei}) \left(2^{-\frac{1.98×10^4}{4.96×10^3}} \right)[/tex]

[tex]\:\:\:\:\:\:\:=2.01×10^{16}\:\text{nuclei}[/tex]

The relation of mass m, angular velocity o and radius of the circular path r of an object with the centripetal force is-
a. F = m²wr
b. F = mwr²
c. F = mw²r
d. F = mwr. ​

Answers

Answer:

Correct option not indicated

Explanation:

There are few mistakes in the question. The angular velocity ought to have been denoted with "ω" and not "o" (as also suggested in the options).

The formula to calculate a centripetal force (F) is

F = mv²/r

Where m is mass, v is velocity and r is radius

where

While the formula to calculate a centrifugal force (F) is

F = mω²r

where m is mass, ω is angular velocity and r is radius of the circular path.

From the above, it can be denoted that the relationship been referred to in the question is that of a centrifugal force and not centripetal force, thus the correct option should be C.

NOTE: Centripetal force is the force required to keep an object moving in a circular path/motion and acts inward towards the centre of rotation while centrifugal force is the force felt by an object in circular motion which acts outward away from the centre of rotation.

Find the amount og work done

Answers

Answer:

100j

Explanation:

Thermometers and Temperature Scales
While traveling outside the United States, you feel sick. A companion gets you a thermometer, which says your temperature is 40.9. What scale is that on? What is your Fahrenheit temperature? Should you seek medical help?

Answers

Answer:

105.62°F

Explanation:

When the body temperature having fever is measured to be 40.9 on a scale then it must be a Celsius scale thermometer because 37°C is the normal temperature of a healthy human. In case of fever the given temperature is measured on a standard Celsius scale.

The relation between Fahrenheit and Celsius scale is:

[tex]\frac{C}{5}=\frac{F-32}{9}[/tex]

[tex]F=\frac{9C}{5} +32[/tex]

[tex]F=105.62^{o}F[/tex]

It is a high fever and an immediate medical help must be taken.

Notice that all the initial spring potential energy was transformed into gravitational potential energy. If you compressed the spring to a distance of 0.200 mm , how far up the slope will an identical ice cube travel before reversing directions

Answers

Answer:

The correct answer will bs "2.41 m".

Explanation:

According to the question,

M = 50 g

or,

   = 0.050 kg

[tex]\Theta = 25^{\circ}[/tex]

k = 25.9 N/m

Δx = 0.200 m

Let the traveled distance be "x".

By using trigonometry, the height will be:

⇒ [tex]h = l Sin \Theta[/tex]

hence,

⇒ [tex]Potential \ energy \ at \ the \ top=Spring \ potential \ energy[/tex]

                                       [tex]Mgh=\frac{1}{2} k(\Delta x)^2[/tex]

By putting the values, we get

             [tex]0.050\times 9.8\times lSin 25^{\circ}=\frac{1}{2}\times 25.0\times (0.200)^2[/tex]

                                              [tex]l=2.41 \ m[/tex]      

what is the dimensional formula of force and torque​

Answers

Answer:

Units. Torque has the dimension of force times distance, symbolically T−2L2M. Although those fundamental dimensions are the same as that for energy or work, official SI literature suggests using the unit newton metre (N⋅m) and never the joule. The unit newton metre is properly denoted N⋅m.

Dimension: M L2T−2

In SI base units: kg⋅m2⋅s−2

Other units: pound-force-feet, lbf⋅inch, ozf⋅in

Answer:

hope it is helpful to you

Julie drives 100 mi to Grandmother's house. On the way to Grandmother's, Julie drives half the distance at 40.0 mph and half the distance at 60.0 mph . On her return trip, she drives half the time at 40.0 mph and half the time at 60.0 mph.

Required:
a. What is Julie's average speed on the way to grandmother's house?
b. What is her average speed in the return trip?

Answers

Answer:

a. The average speed on her way to Grandmother's house is 48.08 mph

b. The average speed in the return trip is 50 mph.

Explanation:

The average speed (S) can be calculated as follows:

[tex] S = \frac{D}{T} [/tex]

Where:

D: is the total distance

T: is the total time

a. To find the total distance in her way to Grandmother's house, we need to find the total time:

[tex]T_{i} = t_{1_{i}} + t_{2_{i}} = \frac{d_{1_{i}}}{v_{1_{i}}} + \frac{d_{2_{i}}}{v_{2_{i}}}[/tex]

Where v is for velocity

[tex] T = \frac{d_{1_{i}}}{v_{1_{i}}} + \frac{d_{2_{i}}}{v_{2_{i}}} = \frac{(100/2) mi}{40.0 mph} + \frac{(100/2) mi}{60.0 mph} = 1.25 h + 0.83 h = 2.08 [/tex]    

Hence, the average speed on her way to Grandmother's house is:

[tex]S_{i} = \frac{D}{T_{i}} = \frac{100 mi}{2.08 h} = 48.08 mph[/tex]

b. Now, to calculate the average speed of the return trip we need to calculate the total time:                        

[tex]D = v_{1_{f}}\frac{T_{f}}{2} + v_{2_{f}}\frac{T_{f}}{2} = \frac{T_{f}}{2}(v_{1_{f}} + v_{2_{f}})[/tex]

[tex]100 mi = \frac{T_{f}}{2}(40 mph + 60 mph)[/tex]

[tex] T_{f} = \frac{200 mi}{40 mph + 60 mph} = 2 h [/tex]

Therefore, the average speed of the return trip is:

[tex]S_{f} = \frac{D}{T_{f}} = \frac{100 mi}{2 h} = 50 mph[/tex]

I hope it helps you!                                                      

An airplane increases its speed at the average rate of 15 m/s2. How much time does it take to increase its speed from 100 m/s to 160 m/s

Answers

Answer:

4 s

Explanation:

Acceleration (a) = 15 m/s²Initial velocity (u) = 100 m/sFinal velocity (v) = 160 m/s

We are asked to calculate time taken (t).

By using the first equation of motion,

[tex]\longrightarrow[/tex] v = u + at

[tex]\longrightarrow[/tex] 160 = 100 + 15t

[tex]\longrightarrow[/tex] 160 - 100 = 15t

[tex]\longrightarrow[/tex] 60 = 15t

[tex]\longrightarrow[/tex] 60 ÷ 15 = t

[tex]\longrightarrow[/tex] 4 s = t

How many neutrons are in an isotope of selenium-83

A. 34
B. 83
C. 49
D. 117

Answers

Answer:

C.49 is yr ans...

hope it helpsstay safe healthy and happy....
I am pretty sure it is 49.

Solids diffuse because the particles cannot move.
A. Can
B. Not enough info
C. Cannot
D. Sometimes will

Answers

Solids cannot diffuse.

Answer: C. Cannot
They don’t space to move.

IS ANYONE THERE..??!​

Answers

Answer:

hmmmmmmmmmmmmmmmmmmmmmmmm y

As you move farther away from a source emitting a pure tone, the ___________ of the sound you hear decreases.

Answers

Answer:

frequency

Explanation:

The phenomenon of apparent change in frequency due to the relation motion between the source and the observer is called Doppler's effect.

So, when we move farther, the frequency of sound decreases. The formula of the Doppler's effect is  

[tex]f' = \frac{v + v_o}{v+ v_s} f[/tex]

where, v is the velocity of sound, vs is the velocity of source and vo is the velocity of observer, f is the true frequency. f' is the apparent frequency.


Question 8 a-e plz

Answers

Answer:

(a) t = 0 s

(b) t = 0 s, 30 s, 55 s

(c) t = 40 s to t = 60 s

(d) t = 10 s to t = 15 s

(e) a = 6 m/s^2

Explanation:

(a) The car is at starting position at t = 0 s and v = 0 m/s.

(b) The velocity of car is zero when the time is t = 0 s, 30 s and 55 s.

(c) from t = 40 s to 60 s the car is moving in the negative direction.

(d) The fastest speed is 60m/s from t = 10 s to t = 15 s.

(e) The slope of the velocity time graph gives acceleration.

a = (60 - 0) / (10 - 0) = 6 m/s^2

The atoms in your body are mostly empty space . And so are the atoms in any wall. Why then is your body unable to pass through walls ?

Answers

First of all, both are not a single sheet of atom. There are many layers of atoms, so the empty part gets beside each other, so there are less empty part. Secondly, there are so many atoms that the probability that they will have empty space at the same place necessary, is negligible.

This was something from logic.

The reason I was taught in my class was that only a limited number of electrons can be in a given orbit, so atoms cannot overlap each other.

What has a wind speed of 240 kph or greater?​

Answers

Answer:

SUPER TYPHOON (STY), a tropical cyclone with maximum wind speed exceeding 220 kph or more than 120 knots.

A body of mass 450g changes it speed from 5ms¹ to 25ms¹. what is the work done by the body?​

Answers

Answer:

135J

Explanation:

So we know ΔKinetic Energy= ΔWork

Kinetic energy=1/2mv²

So Kf-Ki=ΔK

ΔK=1/2*0.45(25²-5²)=135J

135J=ΔWork

During 57 seconds of use, 330 C of charge flow through a microwave oven. Compute the size of the electric current.

Answers

Answer:

5.78amps

Explanation:

Given data

Time t= 57 seconds

Charge Q= 330C

Current I= ??

The expression for the electric current is given as

Q= It

Substituting we have

330= I*57

I= 330/57

I=5.78 amps

Hence the current is 5.78amps

in what part of the plant is glucose suger made?​

Answers

[tex]\large \mid \underline {\bf {{{\color{navy}{Leaf \: \: \: Chloroplast \: ...}}}}} \mid[/tex]

More Information :

Green plants manufacture glucose through a process that requires light, known as photosynthesis.

Glucose is stored in the form of starch in plants.

Why don’t you see tides ( like those of the ocean ) in your swimming pool ?

Answers

In smaller bodies, like your backyard swimming pool, or your own body, the differences of the earth's gravitational force over such small volumes are so slight as to have negligible affect. ... Therefore the tidal bulges move north and south with respect to earth's geography over the course of a year.

d. On the afternoon of January 15, 1919, an unusually warm day in Boston, a 17.7-m-high, 27.4-m-diameter cylindrical metal tank used for storing molasses ruptured. Molasses flooded into the streets in a 5-m-deep stream, killing pedestrians and horses and knocking down buildings. The molasses had a density of 1600 kg>m3 . If the tank was full before the accident, what was the total outward force the molasses exerted on its sides

Answers

Answer:

F = 1.638 x 10⁸ N = 163.8 MN

Explanation:

The total force exerted by the molasses is given as:

F = PA

where,

F = Force exerted by the molasses = ?

P = Pressure = ρgh

ρ = density of molasses = 1600 kg/m³

g = acceleration due to gravity = 9.81 m/s²

h = height of tank = 17.7 m

A = cross-sectional area of tank = πr²

r = radius of tank = 27.4 m/2 = 13.7 m

Therefore,

[tex]F = \rho ghA = \rho gh(\pi r^2)\\\\F = (1600\ kg/m^3)(9.81\ m/s^2)(17.7\ m)(\pi)(13.7\ m)^2[/tex]

F = 1.638 x 10⁸ N = 163.8 MN

When an apple falls towards the earth,the earth moves up to meet the apple. Is this true?If yes, why is the earth's motion not noticeable?

Answers

Answer:

because the mass of the apple is very less compared to the mass of earth. Due to less mass the apple cannot produce noticable acceleration in the earth but the earth which has more mass produces noticable acceleration in the apple. thus we can see apple falling on towards the earth but we cannot see earth moving towards the apple.

If it requires 8.0 J of work to stretch a particular spring by 2.0 cm from its equilibrium length, how much more work will be required to stretch it an additional 4.0 cm

Answers

16 additional J of work
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