It takes a minimum distance of 76.50 m to stop a car moving at 15.0 m/s by applying the brakes (without locking the wheels). Assume that the same frictional forces apply and find the minimum stopping distance when the car is moving at 32.0 m/s.

Answer: See below

Explanation:

Part (a):

As the velocity of the piano is constant, the net force on the piano is zero. The friction is also zero.

Here, F is the force applied by the man towards the inclined plane, mg is the weight of the piano and N is the normal force.

Applying Newton's law we get,

[tex]F = mg\sin \theta[/tex]

Substituting we get,

[tex]F &= \left( {180\;{\rm{kg}}} \right) \times \left( {9.8\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}} \right) \times \sin 19.0^\circ \\ &= 574.3\;{\rm{N}}[/tex]

Therefore, the force is 574.3 N

Part (b)

Here, the force F is applied parallel to the floor.

The friction is zero.

Applying Newton's law we get,

[tex]F\cos \theta &= mg\sin \theta \\ F &= mg\tan \theta[/tex]

Substituting we get,

[tex]F &= \left( {180\;{\rm{kg}}} \right) \times \left( {9.8\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}} \right) \times \tan 19.0^\circ \\ &= 607.4\;{\rm{N}}[/tex]

Therefore, the force is 607.4 N

Explanation:

The total time the ball is in the air is 1.47 s and the maximum horizontal distance covered is 58.7 m.

The time of motion of the ball is calculated as follows;

h = vt + ¹/₂gt²

55 = (50sin37)t + ¹/₂(9.8)t²

55 = 30.1t + 4.9t²

4.9t² + 30.1t - 55 = 0

Solve using formula method;

t = 1.47 s

X = vxt

where;

X = (50 x cos37) x 1.47

X = 58.7 m

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The sentence that uses the subjunctive mood correctly is as follows:

Thus, the correct option is D.

Subjunctive mood may be defined as statements or actions that are in the probable situation of doubt and suspicion.

Except for the sentence fourth, the rest all indicates the factual concept with the appropriate condition.

Therefore, the correct option for this question is D.

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Answer:

C. it is important that she apologize to her sister for what she said

Explanation:

test approved

The time required by the particles are as follows:

a. t = 1.5 seconds

b. t = 3 seconds

c. t = 0.4 seconds

The time required for the particles to be at several distances apart is calculated using the equation of motion given below:

[tex]S = ut + \frac{1}{2}at^{2}[/tex]

a) Time required to be 30 m apart:

Assuming the distance covered by P is S1 and distance covered by Q is S2.

S1 + S2 = 51 - 30

S1 + S2 = 21

Substituting the values of velocity and acceleration in the equation of motion above:

5t + 1/2t^2 + 6t + 3t^2 = 21

2t^2 + 11t - 21 = 0

Solving for time, t by factorization, t = 1.5 seconds

b) Time required to meet:

Assuming the distance covered by P is S1 and distance covered by Q is S2.

S1 + S2 = 51

Substituting the values of velocity and acceleration in the equation of motion above:

5t + 1/2t^2 + 6t + 3t^2 = 51

2t^2 + 11t - 51 = 0

Solving for time, t by factorization, t = 3 seconds

c) Time required for velocity of P is ¾ of the velocity of Q:

Using the equation of motion: V = u + at

Vp = 3/4 Vq

4Vp= 3Vq

Substituting the values:

4(5 + t) = 3(6 + 3t)

5t = 2

t = 0.4 seconds

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Answer:horse

Explanation:

The height of stairs a 60 kg student would have to run in order to burn off 1 Calorie of food energy will be 7.1 meters.

The potential energy is due to the virtue of the position and the height. The unit for the potential energy is the joule.

Given data;

Mass of student,m = 60 kg

Energy,E = 4190 J

Height of stairs,h=?

The potential energy is mainly dependent upon the height of the object. The potential energy is found as;

Potential energy = mgh

E=mgh

h=E/mg

h= 4190 J / (60 kg× 9.81  m/s²)

h = 7.1 metre

Hence the height of the stairs will be 7.1 meters.

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The velocity of the third piece is 124.02 m/s at 1.05⁰ below the horizontal.

The velocity of the third piece is calculated from the principle of conservation of linear momentum.

mu = m₁u₁ + m₂u₂ + m₃u₃

where;

6(22)sin(0) = 2(10)sin32 - 1(8)sin(28) + 3u₃y

0 = 6.84 + 3u₃y

u₃y = -6.84/3

u₃y = -2.28 m/s

ΔP = Pf - Pi = J

where;

2640(0.1) = 2(10)cos32 +  1(8)cos(28) + 3u₃x - 6(22)

264 = -108 + 3u₃x

3u₃x = 372

u₃x = 372/3

u₃x = 124 m/s

u₃ = √(124² + 2.28²)

u₃ = 124.02 m/s

tanθ = u₃y/u₃x

tanθ = 2.28/124

tanθ = 0.018

θ = 1.05⁰ (below the horizontal)

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(a) The work done in moving the unit charge from point C to A is 7.62 x 10⁻³ J.

(b) The work done in moving the unit charge from point D to B is 7.62 x 10⁻³ J.

W = Fd

W = Kq²/d

W(C to A) = W(0 to C) + W(0 to A)

[tex]W(C \ to \ A) = - \frac{Kq^2}{7.07} + \frac{Kq^2}{5} \\\\ W(C \ to \ A) = 0.0586 \ Kq^2\\\\W(C \ to \ A) = 0.0586 \times 9 \times 10^9 \times (3.8\times 10^{-6})^2\\\\W(C \ to \ A) = 7.62 \times 10^{-3} \ J[/tex]

W(D to B) = W(0 to D) + W(0 to B)

W(D to B) = 7.62 x 10⁻³ J

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Answer:

4.2m/s

Explanation:

0.50x8.4=4.2m/s

Answer:

E = 5.52 x 10⁻¹⁹  J

Explanation:

The formula for energy of a photon, E, is:

[tex]E = hf[/tex]

where h is Plank's constant = 6.62 x 10 ⁻³⁴ .

Using the formula:

E = 6.62 x 10⁻³⁴   x   8.34 x 10¹⁴

  = 5.52 x 10⁻¹⁹  J

Answer:

The common velocity v after collision is 2.8m/s²

Explanation:

look at the attachment above ☝️

Answer:

88.761

Explanation:

The variable on the y-axis should be the running speed of hamsters since it is the dependent variable.

The dependent variable is the variable whose value fluctuates depending on other variables in an experiment.

In this case, the running speed is the dependent variable because it depends on the weight of the hamster.

The dependent variable is generally graphed on the Y axes, whereas the independent variable is graphed on the X-axes.

In conclusion, the variable on the y-axis should be the running speed of hamsters since it is the dependent variable.

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The cutoff frequency for magnesium is 8.93 x 10¹⁴ Hz.

The work function is related to the frequency as

W0 = h x fo

where, fo = cutoff frequency and h is the Planck's constant

Given is the work function for magnesium is  3.70 eV.

fo = 3.7 x 1.6 x 10⁻¹⁹ / 6.626 x 10⁻³⁴

fo = 8.93 x 10¹⁴ Hz.

Thus, the cut off frequency is 8.93 x 10¹⁴ Hz.

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If Ross takes two months off from training, his fitness level will reduce in comparison to what it was two months ago.

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In infrared satellite images, land appears black and clouds appear white. C

Infrared satellite images are images produced as a result of electromagnetic radiations reflected or emitted from a target surface in the infrared position of the electromagnetic spectrum.

On infrared images, the clouds emit very bright white color because of the low temperature and the land appears to be black because of the hot temperature.

Therefore, in infrared satellite images, land appears black and clouds appear white. C

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Answer:

1.163 seconds

Explanation:

see the attached. solve the quadratic equation.

Answer:

the anser is b

Explanation:

If the force applied on the object is in the direction of its motion, the speed of the object increases. If the force is applied in the direction opposite to the direction of motion, then it results in a decrease in the speed of the object.

The two factors that affect current carrying capacity of an accumulator will be accumulator size and ambient temperature

Utilizing the compressible and decompressible properties of nitrogen gas, an accumulation vessel is used to store hydraulic pressure.

These key deciding elements are:

1. Accumulator Size: The current capacity increases as the circumference of the conductor increases.

2. Ambient Temperature: The greater the ambient temperature, the less heat is needed to raise the insulation's maximum operating temperature.

3. Accumulator identification:

4. Conditions for Installation:

Hence, the two factors that affect current carrying capacity of an accumulator will be accumulator size and ambient temperature

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Answer:

a community event

Explanation:

a. The value of H is 11.51 m

b. The total kinetic energy as she reaches the ground is 6.21 kJ.

The mechanical energy is the sum of kinetic energy and the potential energy of an object at any instant of time.

M.E = KE +PE

Given is a skier (m=55.0 kg) starts sliding down from the top of a ski jump with negligible friction and takes off horizontally. Value of h = 6.50 m and D = 11.4 m.

Time taken to reach the ground after take off is

t = √2h/g

t = √(2x6.50) /9.81

t =1.15 s

The speed at that time is

speed = distance /time

v = 11.4 /1.15

v = 9.913 m/s

a. From energy conservation principle,

v = √2g(H-h)

Plug the values, we get

9.913 = √(2 x 9.81 (H - 6.5)

Squaring both sides and solving, we have

H = 11.51 m

Thus, the value of H is 11.51 m.

b. The energy at the ground will be only potential energy

Total kinetic energy at the ground = mgH

T.K.E = 55 x 9.81 x 11.51

T.K.E =6.21 kJ

Thus, the total kinetic energy is 6.21 kJ.

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Magnetic stripes provide evidence of seafloor spreading due to their occurrence in the region of sea floor.

When the Earth's magnetic field reverses, a new stripe starts to form. Such magnetic patterns enable the scientist to recognize the occurrence of sea-floor spreading and provides strongest evidence for the theory of plate tectonics.

So we can conclude that magnetic stripes provide evidence of seafloor spreading due to their occurrence in the region of sea floor.

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The number of significant digits to the answer of the following problem is four.

The number of digits rounded to the approximate integer values are called the significant digits.

The following problem is

(2.49303 g) * (2.59 g) / (7.492 g) =

On solving we get

= 0.86184566204

The answer is approximated to  0.86185

Thus, the significant digits must be four.

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The approximate volume of table tennis ball is  80 cm³

Volume is defined as the amount of space occupied by the three dimensional object. S I unit of volume is m³ or cm³.

To find the volume of tennis ball using graduated cylinder.

Step 1 - Fill the graduated cylinder half or full.

Step 2 - Mark the initial volume of the water i.e. 100 cm³ (Vi)

Step 3  - Put the tennis ball in the graduated cylinder. Some of the water was displaced by the table tennis ball.

Step 4 - Mark the Final volume of the water (Vf) i.e. 180 cm³

Step 5 = Calculate the volume by using Formula

Vb = Vf – Vi = 180 cm³ - 100 cm³ = 80 cm³

Hence the volume of tennis ball (Vb) is 80 cm³

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Answer:

40

Explanation:

Answer:

( 688.29 , 276.66 )   meters

Explanation:

Break into horizontal and vertical components

x = 100 cos 55  = 57.36 m/s      

   the x coordinate is then 12 seconds * 57.36 m/s = 688.29 meters

y coordinate is a bit more complex because of the curved path due to gravity

Original y velocity =  100 sin 55

y = vo t - 1/2 (9.81)(t^2)

y =  100 sin 55  (12)  - 1/2 (9.81) (12)^2

      yf = 276.66   meters

Answer:

20 Newtons

Explanation:

10× 2

Answer: A.

2.5 newtons

Explanation: edmentum

This planet's mass must be four times that of Earth in order for the gravitational pull at its surface to be comparable to Earth's.

Newton's law of gravity states that each particle having mass in the universe attracts each other particle with a force known as the gravitational force.

The gravitational force is proportional to the product of the masses of the two bodies and inversely proportional to the square of their distance.

The planet's mass is directly related to its mass at the surface and inversely proportional to the square of its radius;

When mass increases and distance reduces, gravity rises. Gravity also lowers when the distance between two points grows and the mass decreases.

The astronomers discovered a planet twice the size of Earth that resembles Earth.

This planet's mass must be four times that of Earth in order for the gravitational pull at its surface to be comparable to Earth's.

Hence the masses of this planet will be 4 times that of Earth.

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(a) The time taken the block to reach the ground once it flies off the edge of the table is 0.47 s.

(b) The initial horizontal velocity of the block as it flies off the table is 3.91 m/s.

(c) The initial speed of the bullet is 237.5 m/s.

The time of motion of the block is calculated as follows;

h = ¹/₂gt²

where;

t = √(2h/g)

t = √( (2 x 1.08) / 9.8)

t = 0.47 s

x = vt

v = x/t

v = (1.84)/(0.47)

v = 3.91 m/s

m1u1 + m2u2 = v(m1 + m2)

where;

0.00611(u1) + 0.365(0) = 3.91(0.00611 + 0.365)

0.00611u1 = 1.451

u1 = 1.451/0.00611

u1 = 237.5 m/s

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