A turntable rotates with a constant 1.85 rad/s2 clockwise angular acceleration. After 4.00 s it has rotated through a clockwise angle of 30.0 rad . Part A What was the angular velocity of the wheel at the beginning of the 4.00 s interval?

Complete Question

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Answer:

The distance is [tex]r_2 = 4 \ AU[/tex]

Explanation:

From the question we are told that

    The size of Jupiter is  [tex]s_2 = 143,000 \ km[/tex]

    The  length of the International Space Station is [tex]r_1 = 380\ km[/tex]

    The  size of the International Space Station is  [tex]s_1 = 90 \ m =0.09 \ km[/tex]

The angular size where the same one night and this angular size is mathematically represented as

      [tex]\theta = \frac{s}{r}[/tex]

Since  [tex]\theta[/tex] is constant

        [tex]\frac{s_1}{r_1} = \frac{s_2}{r_2}[/tex]

substituting values

      [tex]\frac{0.09}{380} = \frac{143000}{r_2}[/tex]

=>   [tex]r_2 = 6.04 * 10^{9} \ km[/tex]

Now we are told to convert to AU and  1 AU  [tex]= 1.5 * 10^8 \ km[/tex]

  So

      [tex]r_2 = \frac{6.04 * 10^8}{1.5*10^{8}}[/tex]

      [tex]r_2 = 4 \ AU[/tex]

Answer:

2.95m

Explanation:

The farthest distance the object can move is the radius of the circle of which the Simple harmonic motion is assumed to be a part

But V = w× r; where V is velocity,

w is angular velocity and r is radius.

Also,

a= w2r; where a is linear acceleration

but a = v× r ; by comparing both equations

Hence r = a/v =8.6/2.45 =3.51m

But the horizontal distance of the motion is given by:

X = rcosx ; where x is the angle

X is the distance covered.

We know that the maximum value of cos x is 1 which is 0°

When the object moves in a fashion directly parallel to an horizontal distance, maximum distance would be reached and hence:

X = r=3.51m

Meaning the object needs to travel 3.51-0.56=2.95m further.

Note: the acceleration of the motion is constant whether it is swinging towards the left or right.

When the object is displaced 0.560 m to the right of its equilibrium position, it has a velocity of 2.45 m/s to the right and an acceleration of 8.60 m/s2 to the left and the amplitude of motion A = 0.732 m.

The distance between the central and extreme points for a moving particle is known as the amplitude of motion.

The given data to find the amplitude of motion,

Object displaced = 0.560 m

Velocity = 2.45 m/s

Acceleration = 8.60 m/s²

Starting with sine:

x(t) = Asin(ωt)

so that t = 0, x = 0

x(t) = 0.56 m = Asin(ωt)

v(t) = x(t)'= 2.45 m/s = Aωcos(ωt)

a(t) = v(t)'= -8.60 m/s² = -Aω²sin(ωt)

x(t) / a(t) = Asin(ωt) / -Aω²sin(ωt)

0.56m / -8.60 m/s² = -1 / ω²

ω² = 15.3571 rad^2/s^2

ω = 3.91881 rad/s  

x(t) / v(t) = Asin(ωt) / Aωcos(ωt)

0.560m / 2.45m/s = tan(3.91t) / 3.91rad/s

0.8937= tan(3.91t)

t = 0.176 s  

x(0.176) = Asin(3.59×0.176)

0.65 m= Asin(0.631)

A = 0.732 m is the amplitude of motion.

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Answer:

The correct answer is option (c) a success because it did not detect a shift in the interference pattern.

Explanation:

In Michelson and Morley experiment  it was considered to be successful.

They both found out that the experiment that was carried out was not a failure  since it did not detect any shift in the interference pattern.

With this findings it was widely regarded as correct and precise.

Answer:

The correct answer is a

Explanation:

The cosine function is

      cos θ = ca / ​​H

done ca is the adjacent leg (x-axis) and H is the hypotenuse (vector module)

we clear

    H = ca / ​​cos θ

therefore, to find the magnitude of the vector, the cathete is divided into the cosine.

The correct answer is a

Answer:

The initial angular speed is [tex]w_i = 48 \ rad/s[/tex]

Explanation:

From the question we are told that

   The angular displacement is  [tex]\theta = 220 \ rad[/tex]

    The angular speed is  [tex]w_f = 92 \ rad/s[/tex]

    The acceleration is  [tex]\alpha = 14 \ rad/s^2[/tex]

Generally the initial angular speed can be evaluated as

     [tex]w_f ^2 = w_i ^2 + 2 * \alpha * \theta[/tex]

=>  [tex]w_i ^2 = w_f ^2 - 2 * \alpha * \theta[/tex]

substituting values

=>     [tex]w_i ^2 = 92 ^2 - 2 * 14 * 220[/tex]

=>      [tex]w_i ^2 = 2304[/tex]

=>     [tex]w_i = 48 \ rad/s[/tex]

Answer:

a) v = 1.075*10^7 m/s

b) FB = 7.57*10^-12 N

c) r = 10.1 cm

Explanation:

(a) To find the speed of the alpha particle you use the following formula for the kinetic energy:

[tex]K=qV[/tex]          (1)

q: charge of the particle = 2e = 2(1.6*10^-19 C) = 3.2*10^-19 C

V: potential difference = 1.2*10^6 V

You replace the values of the parameters in the equation (1):

[tex]K=(3.2*10^{-19}C)(1.2*10^6V)=3.84*10^{-13}J[/tex]

The kinetic energy of the particle is also:

[tex]K=\frac{1}{2}mv^2[/tex]       (2)

m: mass of the particle = 6.64*10^⁻27 kg

You solve the last equation for v:

[tex]v=\sqrt{\frac{2K}{m}}=\sqrt{\frac{2(3.84*10^{-13}J)}{6.64*10^{-27}kg}}\\\\v=1.075*10^7\frac{m}{s}[/tex]

the sped of the alpha particle is 1.075*10^6 m/s

b) The magnetic force on the particle is given by:

[tex]|F_B|=qvBsin(\theta)[/tex]

B: magnitude of the magnetic field = 2.2 T

The direction of the motion of the particle is perpendicular to the direction of the magnetic field. Then sinθ = 1

[tex]|F_B|=(3.2*10^{-19}C)(1.075*10^6m/s)(2.2T)=7.57*10^{-12}N[/tex]

the force exerted by the magnetic field on the particle is 7.57*10^-12 N

c) The particle describes a circumference with a radius given by:

[tex]r=\frac{mv}{qB}=\frac{(6.64*10^{-27}kg)(1.075*10^7m/s)}{(3.2*10^{-19}C)(2.2T)}\\\\r=0.101m=10.1cm[/tex]

the radius of the trajectory of the electron is 10.1 cm

The speed, magnetic force and radius are respectively; 10.75 * 10⁶ m/s; 7.57 * 10⁻¹² N; 0.101 m

A) We know that the formula for kinetic energy can be expressed as;

K = qV

where;

q is charge of the particle = 2e = 2(1.6 × 10⁻¹⁹ C) = 3.2 × 10⁻¹⁹ C

V is potential difference = 1.2 × 10⁶ V

K = 3.2 × 10⁻¹⁹ *  1.2 × 10⁶

K = 3.84 × 10⁻¹³ J

Also, formula for kinetic energy is;

K = ¹/₂mv²

where v is speed

Thus;

v = √(2K/m)

v = √(2 * 3.84 × 10⁻¹³)/(6.64 * 10⁻²⁷)

v = 10.75 * 10⁶ m/s

B) The magnetic force is given by the formula;

F_b = qvB

F_b = (3.2 × 10⁻¹⁹ * 10.75 * 10⁶ * 2.2)

F_b = 7.57 * 10⁻¹² N

C) The formula to find the radius is;

r = mv/qB

r = (6.64 * 10⁻²⁷ * 10.75 * 10⁶)/(1.6 × 10⁻¹⁹ * 2.2)

r = 0.101 m

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Answer:

  More than 48%

Explanation:

If the interest is computed monthly on the outstanding balance, it has an effective annual rate of ...

  (1 +4%)^12 -1 = 60.1% . . . .  more than 48%

The effective annual or yearly interest rate would be=30.56% which is Between 4% and 48%

The formula used to calculate annual Interest rate =

[tex](1+ \frac{i}{n} ) {}^{n} - 1[/tex]

where i= nominal interest rate = 4%

n= number of periods= 12 months

Annual Interest rate=

[tex](1 + \frac{4\%}{12} ) {}^{12} - 1[/tex]

= (1+0.333)^12 -1

= (1.333)^12-1

= 31.56 - 1

= 30.56%

Therefore, the effective annual or yearly interest rate would be= 30.56%

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Answer:

ΔL = 1.011 mm

Explanation:

Let's begin by listing out the given information:

Length (L) = 600 mm = 0.6 m,

Diameter (D) = 40 mm = 0.04 m ⇒ Radius (r) = 20 mm = 0.2 m,

Area (cross sectional) = πr² = 3.14 x .02² = 0.001256 m²,

Modulus of Elasticity (E) = 85 GN/m²,

Compressive load (F) = 180 KN

Using the formula, Stress = Load ÷ Area

Mathematically,

σ = F ÷ A = 180 x 10³ ÷ 0.001256

σ = 143312.1 KN/m²

Modulus of elasticity = stress ÷ strain

E = σ ÷ ε

ε = ΔL/L

85 x 10⁹ = 143312.1 x 10³ ÷ (ΔL/L)

ΔL = 143312.1 x 10³ ÷ 85 X 10⁹ = 1686.02 * 10⁻⁶

ΔL = L x 1686.02 * 10⁻⁶

ΔL = 0.6 * 1686.02 * 10⁻⁶ = 1011.61 x 10⁻⁶

ΔL = 1.011 x 10⁻³ m

ΔL = 1.011 mm

∴The bar contracts by 1.011 mm

The dragster's velocity v at time t with constant acceleration a is

[tex]v=at[/tex]

since it starts at rest.

After 2.1 s, it will attain a velocity of

[tex]v=\left(44.0\dfrac{\rm m}{\mathrm s^2}\right)(2.1\,\mathrm s)[/tex]

or 92.4 m/s.

Doubling the time would double the final velocity,

[tex]v=a(2t)=2at[/tex]

so the velocity would be twice the previous one, 184.8 m/s.

The dragster undergoes a displacement x after time t with acceleration a of

[tex]x=\dfrac12at^2[/tex]

if we take the starting line to be the origin.

After 2.1 s, it will have moved

[tex]x=\dfrac12\left(44.0\dfrac{\rm m}{\mathrm s^2}\right)(2.1\,\mathrm s)^2[/tex]

or 88 m.

Doubling the time has the effect of quadrupling the displacement, since

[tex]x=\dfrac12a(2t)^2=4\left(\dfrac12at^2\right)[/tex]

so after 4.2 s it will have moved 352 m.

Answer:

A.  xmax = 131.49 m

B.  t = 8.74 s

C.  ymax = 220.33 m

Explanation:

A. In order to find the horizontal distance which cannon travels you first calculate the flight time. The flight time can be calculated by using the following formula:

[tex]y=y_o+v_osin\theta-\frac{1}{2}gt^2[/tex]      (1)

yo: height from the projectile is fired = 200m

vo: initial velocity of the projectile = 25m/s

g: gravitational acceleration = 9.8 m/s^2

θ: angle between the direction of the initial motion of the ball and the horizontal = 53°

t: time

You need the value of t when the projectile hits the ground. Then, in th equation (1) you make y = 0m.

When you replace the values of all parameters in the equation (1), you obtain the following quadratic formula:

[tex]0=200+(25)sin53\°t-\frac{1}{2}(9.8)t^2\\\\0=200+19.96t-4.9t^2[/tex] (2)

You use the quadratic formula to obtain the value of t:

[tex]t_{1,2}=\frac{-19.96\pm\sqrt{(19.96)^2-4(-4.9)(200)}}{2(-4.9)}\\\\t_{1,2}=\frac{-19.96\pm65.71}{-9.8}\\\\t_1=8.74s\\\\t_2=-4.66s[/tex]

You use the positive value because it has physical meaning.

Now, you can calculate the horizontal range of the projectile by using the following formula:

[tex]x_{max}=v_ocos\theta t[/tex]      

[tex]x_{max}=(25m/s)(cos53\°)(8.74s)=131.49m[/tex]

The cannon ball travels a horizontal distance of 131.49 m

B. The cannon ball reaches the canon for t = 8.74s

C. The maximum height is obtained by using the following formula:

[tex]y_{max}=y_o+\frac{v_o^2sin^2\theta}{2g}[/tex]     (3)

By replacing in the equation (3) the values of all parameters you obtain:

[tex]y_{max}=200m+\frac{(25m/s)^2(sin53\°)^2}{2(9.8m/s^2)}\\\\y_{mac}=200m+20.33m=220.33m[/tex]

The maximum height reached by the cannon ball is 220.33m

Answer:

The apparent weight of the person as she pass the highest point is  [tex]N = 458.8 \ N[/tex]

Explanation:

From the question we are told that

   The radius of the Ferris wheel is [tex]r = 5.0 \ m[/tex]

    The period of revolution is [tex]T = 8.0 \ s[/tex]

     The weight of the person is  [tex]W = 670 \ N[/tex]

Generally the speed of the wheel is mathematically represented as

      [tex]v = \frac{2 \pi r}{T }[/tex]

substituting values

      [tex]v = \frac{2 * 3.142 * 5}{8 }[/tex]

       [tex]v = 3.9 3 \ m/s[/tex]

The apparent weight (the normal force exerted on her by the bench) at the highest point is mathematically evaluated as

          [tex]N = mg - \frac{mv^2}{r}[/tex]

Where m is the mass of the person which is mathematically evaluated as

     [tex]m = \frac{W}{g}[/tex]

substituting values

    [tex]m = \frac{670}{9.8}[/tex]

    [tex]m = 68.37 \ kg[/tex]

So

    [tex]N = 68.37 * 9.8 - \frac{68.37 * {3.93}^2}{5}[/tex]

    [tex]N = 458.8 \ N[/tex]

Answer:

A) 580m

B) 0 m/s

C) 9.8m/s^2

D) downward

E) 10.87s

F) 106.62 m/s

Explanation:

A) The distance traveled by the rocket is calculated by using the following expression:

[tex]y=\frac{1}{2}at^2[/tex]

a: acceleration of the rocket = 2.90 m/s^2

t: time of the flight = 20.0 s

[tex]y=\frac{1}{2}(2.90\frac{m}{s^2})(20.0s)^2=580m[/tex]

B) In the highest point the rocket has a velocity with magnitude zero v = 0m/s because there the rocket stops.

C) The engines of the rocket suddenly fails in the highest point. There, the acceleration of the rocket is due to the gravitational force, that is 9.8 m/s^2

D) The acceleration points downward

E) The time the rocket takes to return to the ground is given by:

[tex]t=\sqrt{\frac{2y}{g}}=\sqrt{\frac{2(580m)}{9.8m/s^2}}=10.87s[/tex]

10.87 seconds

F) The velocity just before the rocket arrives to the ground is:

[tex]v=\sqrt{2gy}=\sqrt{2(9.8m/s ^2)(580m)}=106.62\frac{m}{s}[/tex]

Answer:

0.173 N.

Explanation:

We will calculate the mass and then use the following calculations on the surface of planet X that is :

                           [tex]W=mg[/tex]

We would use the following equation to get the value of g for planet X that is :

                   [tex]y_f-y_i=v_{yi}t+\frac{1}{2}gt^2[/tex]

Then, put the values in the above equation.

                          [tex]16=0+\frac{1}{2}\times g\times(2.90)^2[/tex]

                           [tex]\bf\mathit{g=3.80\;m/s^2}[/tex]

Now, we will measure the ball weight on planet X's surface:

                          [tex]m=\frac{100}{1000} \;\;\;\;\;\;\;\;\;\;[1kg=1000g][/tex]

Then, we have to put the value in the above equation.

                        [tex]W=0.1\times 1.73=0.173\:N[/tex]

Answer:

Energy Stored = 36000 J = 36 KJ

Explanation:

The power of a battery is given by the formula:

P = IV

where,

P = Power delivered by the battery

I = Current Supplied to the battery

V = Potential Difference between terminals of battery = 12 volt

Now, we multiply both sides by the time period (t):

Pt = VIt

where,

Pt = (Power)(Time) = Energy Stored = E = ?

It = Battery Current Rating = 50 A.min

Converting this to A.sec;

It = Battery Current Rating = (50 A.min)(60 sec/min) = 3000 A.sec

Therefore,

E = (12 volt)(3000 A.sec)

E = 36000 J = 36 KJ

Answer:

Work-done in quarter an hour = 3.5 × 10⁶ J

Explanation:

Given:

Force (F) = 280 KN = 280,000 N

Velocity (V) = 50 km / h

Time (t) = 1 / 4 = 0.25 hour

Find:

Work-done in quarter an hour

Computation:

⇒ Displacement = Velocity (V) × Time

⇒ Displacement = 50 × 0.25

⇒ Displacement = 12.5 km

⇒ Work-done = Force (F) × Displacement

⇒ Work-done in quarter an hour = 280,000 × 12.5

⇒ Work-done in quarter an hour = 3,500,000

Work-done in quarter an hour = 3.5 × 10⁶ J

Answer:

Vbg = 20.5 m/s

your velocity with respect to the ground Vbg = 20.5 m/s

Explanation:

Relative velocity with respect to the ground is;

Vbg = velocity of train with respect to the ground + your velocity with respect to the train

Vbg = Vtg + Vbt ......1

Given;

velocity of train with respect to the ground;

Vtg = 19 m/s

your velocity with respect to the train;

Vbt = 1.5 m/s

Substituting the given values into the equation 1;

Vbg = 19 m/s + 1.5 m/s

Vbg = 20.5 m/s

your velocity with respect to the ground Vbg = 20.5 m/s

Answer:

a) [tex]F = 210.803\,N[/tex], b) [tex]W_{F} = 779.971\,J[/tex], c) [tex]W_{f} = 235.683\,J[/tex], d) [tex]W_{N} = 0\,J[/tex]; [tex]W_{g} = 544.289\,J[/tex], e) [tex]W_{net} = 0\,J[/tex]

Explanation:

a) The net force exerted on the crate is:

[tex]\Sigma F = F - m\cdot g \cdot \sin \theta - \mu_{k}\cdot m\cdot g \cdot \cos \theta = 0[/tex]

The magnitud of the force that the work must apply to the crate is:

[tex]F = m\cdot g \cdot \sin \theta + \mu_{k}\cdot m\cdot g \cdot \cos \theta[/tex]

[tex]F = (30\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot \sin 30^{\circ} + 0.25 \cdot (30\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot \cos 30^{\circ}[/tex]

[tex]F = 210.803\,N[/tex]

b) The work done on the crate due to the external force is:

[tex]W_{F} = (210.803\,N)\cdot (3.7\,m)[/tex]

[tex]W_{F} = 779.971\,J[/tex]

c) The work done on the crate due to the external force is:

[tex]W_{f} = (63.698\,N)\cdot (3.7\,m)[/tex]

[tex]W_{f} = 235.683\,J[/tex]

d) The work done on the crate due the normal force is zero, since such force is perpendicular to the motion direction.

[tex]W_{N} = 0\,J[/tex]

And, the work done by gravity is:

[tex]W_{g} = (147.105\,N)\cdot (3.7\,m)[/tex]

[tex]W_{g} = 544.289\,J[/tex]

e) Lastly, the total work done is:

[tex]W_{net} = W_{F} - W_{f} - W_{g} - W_{N}[/tex]

[tex]W_{net} = 779.971\,J - 235.683\,J - 0\,N - 544.289\,J[/tex]

[tex]W_{net} = 0\,J[/tex]

Answer:

K = 3.9 kJ

Explanation:

The kinetic energy ([tex]K_{T}[/tex]) added is given by the difference between the final kinetic energy and the initial kinetic energy:

[tex] K_{T} = K_{f} - K_{i} [/tex]  

The initial kinetic energy is:

[tex] K_{i} = \frac{1}{2}m_{1}v_{1}^{2} [/tex]

Where m₁ is the mass of the object before the explosion and v₁ is its velocity

[tex] K_{i} = \frac{1}{2}m_{1}v_{1}^{2} = \frac{1}{2}70 kg*(21 m/s)^{2} = 1.54 \cdot 10^{4} J [/tex]

Now, the final kinetic energy is:

[tex] K_{f} = \frac{1}{2}m_{2}v_{2}^{2} + \frac{1}{2}m_{3}v_{3}^{2} [/tex]

Where m₂ and m₃ are the masses of the 2 pieces produced by the explosion and v₁ and v₂ are the speeds of these pieces

Since m₂ is 4 times as massive as m₃ and v₃ = 0, we have:

[tex] K_{f} = \frac{1}{2}*\frac{4}{5}m_{1}v_{2}^{2} + \frac{1}{2}*\frac{1}{5}m_{1}*0 [/tex]   (1)          

By conservation of momentum we have:

[tex] p_{i} = p_{f} [/tex]

[tex] m_{1}v_{1} = m_{2}v_{2} + m_{3}v_{3} [/tex]  

[tex] m_{1}v_{1} = \frac{4}{5}m_{1}v_{2} + \frac{1}{5}m_{1}*0 [/tex]

[tex] v_{2} = \frac{5}{4}v_{1} [/tex]     (2)

By entering (2) into (1) we have:

[tex] K_{f} = \frac{1}{2}*\frac{4}{5}m_{1}(\frac{5}{4}v_{1})^{2} = \frac{1}{2}*\frac{4}{5}70 kg(\frac{5}{4}*21 m/s)^{2} = 1.93 \cdot 10^{4} J [/tex]  

Hence, the kinetic energy added is:

[tex] K_{T} = K_{f} - K_{i} = 1.93 \cdot 10^{4} J - 1.54 \cdot 10^{4} J = 3.9 \cdot 10^{3} J [/tex]  

Therefore, the kinetic energy added to the system during the explosion is 3.9 kJ.

I hope it helps you!

Answer:

I can help! What level of physics is it and what are your main topics?

Answer:

91.5 miles

Explanation:

61 miles per hour so 61(x amount of hours)

so 61 x 1.5 hours is 91.5 miles

Complete Question

The complete question is shown on the first uploaded image

Answer:

The mass is    [tex]M =1.43 *10^{32} \ kg[/tex]

Explanation:

From the  question we are told that

       The mass of the stars are [tex]m_1 = m_2 =M[/tex]

        The orbital speed of each star is  [tex]v_s = 240 \ km/s =240000 \ m/s[/tex]

         The orbital period is [tex]T = 12.5 \ days = 12.5 * 2 4 * 60 *60 = 1080000\ s[/tex]

The centripetal force acting on these stars is mathematically represented as

      [tex]F_c = \frac{Mv^2}{r}[/tex]

The gravitational force acting on these stars is mathematically represented as

      [tex]F_g = \frac{GM^2 }{d^2}[/tex]

So  [tex]F_c = F_g[/tex]

=>        [tex]\frac{mv^2}{r} = \frac{Gm_1 * m_2 }{d^2}[/tex]

=>      [tex]\frac{v^2}{r} = \frac{GM}{(2r)^2}[/tex]

=>      [tex]\frac{v^2}{r} = \frac{GM}{4r^2}[/tex]

=>    [tex]M = \frac{v^2*4r}{G}[/tex]

The distance traveled by each sun in one cycle is mathematically represented as

     [tex]D = v * T[/tex]

      [tex]D = 240000 * 1080000[/tex]

      [tex]D = 2.592*10^{11} \ m[/tex]

Now this can also be represented as

      [tex]D = 2 \pi r[/tex]

Therefore

                  [tex]2 \pi r= 2.592*10^{11} \ m[/tex]

=>   [tex]r= \frac{2.592*10^{11}}{2 \pi }[/tex]

=>    [tex]r= 4.124 *10^{10} \ m[/tex]

So  

       [tex]M = \frac{v^2*4r}{G}[/tex]

=>    [tex]M = \frac{(240000)^2*4*(4.124*10^{10})}{6.67*10^{-11}}[/tex]

=>    [tex]M =1.43 *10^{32} \ kg[/tex]

Answer:

At thestratosphere: it 20- 25km

Answer:

About 2104m/s

Explanation:

[tex]F=ma \\\\F=\dfrac{2660kg}{2}\cdot 1614m/s=2,146,620N \\\\2,146,620N=1,269kg\cdot a \\\\a\approx 1691m/s \\\\v_f=v_o+at=413m/s+1691m/s=2104m/s[/tex]

Hope this helps!

Answer:

The width of the river is  [tex]z = 60.62 \ m[/tex]

Explanation:

From the question we are told that

     The distance of the base line is D = 130 m

       The angle is  [tex]\theta = 25^o[/tex]

A diagram illustration the question is shown on the first uploaded image

    Applying Trigonometric Rules for Right-angled Triangle,

            [tex]tan 25 = \frac{z}{130}[/tex]

Now making  z the subject

           [tex]z = 130 * tan (25)[/tex]

          [tex]z = 60.62 \ m[/tex]

Answer:5.35nm

Explanation:

Consider that 1 inch is = 0.0254m

we have,

1m= 1x10^9 nm  

While:

0.0254m = 2.54x10^7nm  

1/55 (2.54x10^7) = 4.6181 x 10^5nm  

1 day= 24 hrs  

= (24x60) when calculating in min  

= (24x60x60) calculating in seconds we have:

= 8.64x10⁴sec  

In 8.64x10^4 seconds, the hair grows by 4.6181 x 10^5nm

Therefore, the amount by which the hair grows in 1 second  will be;

= (4.6181 x 10^5)/(8.64x10^4)  

= 5.35nm  

The rate of growth will be 5.35nm

Answer:

a. 2.668 m/s

b. 0.00494

Explanation:

The computation is shown below:

a. As we know that

[tex]W = F\times d[/tex]

[tex]KE = 0.5\times m\times v^2[/tex]

As the wind does not move the skater to the east little work is performed in this direction. All the work goes in the direction of the N-S. And located in that direction the component of the Force.

F = 3.70 cos 45 = 2.62 N

[tex]W = F \times d = 2.62 N \times 100 m[/tex]

[tex]W = 261.6 N\times m[/tex]

We know that

KE1 = Initial kinetic energy

KE2 = kinetic energy following 100 m

The energy following 100 meters equivalent to the initial kinetic energy less the energy lost to the work performed by the wind on the skater.

So, the equation is

KE2 = KE1 - W

[tex]0.5 m\times v2^2 = 0.5 m\ v1^2 - W[/tex]

Now solve for v2

[tex]v2 = \sqrt{v1^2 - {\frac{2W}{M}}}[/tex]

[tex]= \sqrt{4.1 m/s)^2 - \frac{2 \times 261.6 N\times m}{54.0 kg}}[/tex]

= 2.668 m/s

b. Now the minimum value of Ug is

As we know that

Ff = force of friction

Us = coefficient of static friction

N = Normal force = weight of skater

So,

[tex]Ff = Us\times N[/tex]

Now solve for Us

[tex]= \frac{Ff}{N}[/tex]

[tex]= \frac{3.70 N \times cos 45 }{54.0 kg \times 9.81 m/s^2}[/tex]

= 0.00494

Answer:

Tilted forward to keep the driest.

Explanation:

The rain is falling vertically so there is no wind. In these circumstances the umbrella should be tilted vertically forward.

The situation is the same as if you would stand still and the rain would come under an angle from the front.

Answer:

v = 19.2 m/s

Explanation:

In order to find the speed of the string you use the following formula:

[tex]f=\frac{v}{2L}[/tex]          (1)

f: frequency of the string = 80.0Hz

v: speed of the wave = ?

L: length of the string = 12.0cm = 0.12m

The length of the string coincides with the wavelength of the wave for the fundamental mode.

Then, you solve for v in the equation (1), and replace the values of the other parameters:

[tex]v=2Lf=2(0.12m)(80.0Hz)=19.2\frac{m}{s}[/tex]

The speed of the wave is 19.2 m/s