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The ball will take 3 seconds to get to the top of its trajectory When it is launched from the ground with a horizontal speed of 30 m/s and a vertical speed of 30 m/s

When any object is thrown from horizontal at an angle θ except 90°, then the path followed by it is called trajectory, the object is called projectile and its motion is called projectile motion.

Here, we have a type of motion called projectile motion and it is pretty similar to an upside down parabola. The top of the trajectory is the vertex of the parabola and is also when v = 0.

Given :

This problem is now relatively easy because we only need to find the vertical distance so we can ignore horizontal speed and use

vy = vy0 + ayt

Plug in our givens

0 = 30  - 10t

solve for t

t = 3 seconds

Hence, The ball will take 3 seconds to get to the top of its trajectory When it is launched from the ground with a horizontal speed of 30 m/s and a vertical speed of 30 m/s

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Answer:

M = 3.5 kg         mass of object

F = - K x     where K is the spring constant

K = 144 N/m

ω = (K/M)^1/2     for simple harmonic motiom

ω = (144 kg/s^2 / 3.5 kg)^1/2 = 6.41 / sec

f =  ω / (2 * π)  = 1 / P

P = (2 Π / ω) = 2 * 3.14 / 6.41 sec

P = .98 sec

Check: f = 1 / P = 1.02 /sec

ω = 2 * π * f = 2 * 3.14 * 1.02 = 6.41 sec

Answer:

The total momentum of a system is conserved only when the system is closed.

Explanation:

Answer:

Because of the knowledge of relative size, it will be assumed that the smaller jetliner is farther away.

Explanation:

According to the theory of relative size, the distance that an object has to the viewing individual affects the perception of the individual regarding the size of the object.

As stated in this case, one of the jetliners is farther away from the other. Therefore, even if the jets are of equal size, the one that is at a greater distance is perceived to be smaller as it is at a greater viewing range. The one that is nearer to the individual seems bigger in comparison to the one farther away due to a closer viewing range.

Therefore, the jet that is nearer appears larger.

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The maximum potential energy of the car or the when car is not moving at points A and E; option A.

Potential energy is the energy of a body due to its state or position.

In the rollercoaster motion shown, the maximum potential energy occurs when the car is no longer moving.

At different points other than at maximum potential energy, the energy is a combination of potential and kinetic energy.

The maximum potential energy occurs at A and E, at which point the car is not moving.

In conclusion, at maximum potential energy, the car is not moving.

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Mass is 77,000 g

The density of a certain type of plastic = 0.77 [tex]$\mathrm{g} / \mathrm{cm}^{3}$[/tex]

Length = 10.0 m = 1000 cm

Width = 1 m = 100 cm

Thickness = 1 cm

Volume = length x width x thickness

Mass = Density x Volume

Density

Volume V = 1000 x 100 x 1

             V = 100,000 [tex]cm^{2}[/tex]

Mass M= 0.77 [tex]$\mathrm{g} / \mathrm{cm}^{3}$[/tex] x 100,000 [tex]cm^{2}[/tex]

M = 77,000 g

So, Mass is 77,000 g

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The net force acting on test charge is resultant of two force i.e.,  √2 F

The magnitude of force on test charge due to one charge Q is:

                F = k qQ / r²

where k = 9 × 10^9

Similarly the force due to second charge will be:

         F = k qQ / r²

Now both the charges of magnitude Q is present and it is pointed at right angle to each other then the force  will be resultant i.e.,

                    F = √ F² + F² = F√2

 Hence, net force acting on test charge is √2 F.

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Answer:

The correct choice is 8o.

Explanation:

The given weight is hanging at the mid point of the rope and the buildings are at the same level, Obtain the given equation by equating the vertical components of force,

2Tsin(φ)=W

where φ is the angle made by rope with the horizontal.

Given T=1800 N and W=500 N, the value of φ is calculated as follows,

2*1800*sin(φ)=500

sin(φ)=0.1388

φ=7.90

φ≈8o

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The frictional force on the body is  0.25 N the net force on the body is  5.95 N while the acceleration produced is 2.83 m/s^2

The net force is used to describe the resultant force that acts on the object.

The frictional force that acts on the object s obtained from;

Ff = 0.15 * 2.1-kg * 9.8 m/s^2

Ff = 0.25 N

The net force that acts on the body = F - Ff where F is the applied the force

=  6.2 N - 0.25 N

Net force = 5.95 N

Now;

Net force = ma

a= Net force /m

a = 5.95 N/2.1-kg

a = 2.83 m/s^2

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Answer: A Brightfield microscope equipped with an opaque light stop is able to block light from the illuminator and creating bright objects on a dark background.

Explanation: To find the correct statement about Brightfield microscope, we need to know more about the Brightfield microscope.

Thus, we can conclude that, A Brightfield microscope equipped with an opaque light stop is able to block light from the illuminator and creating bright objects on a dark background.

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Another way to keep food warm till you arrive at the hospital is by putting the food in a foil and wrapping it up with a towel to retain the heat.

Food preservation is defined as the process by which a cooked food or process food is kept in such a way that microorganisms cannot affect their taste and texture.

To prevent a cooked food from getting cold, you can put the food in an aluminium foil and wrap it with a towel to prevent heat loss.

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Answer:

900 km/hr = 9E5 m / 3600 sec = 250 m/sec

ah = v^2 / R = 250^2 m/s / 1000 m = 62.5 m/s^2   horizontal acceleration

av = 9.8 m/s^2      vertical acceleration (due to gravity)

ah / av = 62.5 / 9.8 = 6.38   centripetal acceleration is greater

Answer:

If the ray of light is deflected by 45 degrees by the first mirror its total deflection by mirror (I) is 90 deg. (incident = 45 and exit ray equals 45 deg)

The second mirror will cause a net deflection of 90 degrees and the total deflection will be 180 deg or in opposite  direction to the  incident ray.

Assumed that resistors are connected in series .

Current=I

The statement which is true about a piece of ice at 0°C which is put into a freezer at -18°C is it having the temperature of the freezer.

This is referred to the degree of hotness or coldness of a body and the unit is Celsius or Kelvin.

The ice at 0°C will experience a change in temperature of the freezer when put in it in this scenario.

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3.if time=45mins,D=4km,2700secs,4000m then. S=d/t S=1.4m/s

Her acceleration on the rough patch is 2.8m/s².

To find the answer, we need to know about the Newton's equation of motion.

These are as follows

V= Final velocity

U = initial velocity

t= time

S= distance

36-64 = 10a

-28= 10 a

a= -28/10= -2.8 m/s²

Thus, we can conclude that the acceleration on the patch is 2.8 m/s².

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Using the idea of motion under gravity, it will take 0.5 seconds more before the phone hits the ground.

The distance covered is obtained form the equations of kinematics under gravity.

Now;

v = u + gt

Recall that it was dropped from a height hence u = 0 m/s

v = gt

v = 9.8 m/s^2 * 4 s

v = 39.2 m/s

Now;

h = ut + 1/2gt^2

but u = 0 m/s

h = 1/2gt^2

h = 1/2 * 9.8 * (4)^2

h = 78.4 m

The phone  will not hit the ground within this time

For the phone to hit the ground;

h = 1/2gt^2

if h = 100 m

100 = 1/2 * 9.8 * t^2

2 * 100/9.8 =  t^2

t = √2 * 100/9.8

t = 4.5 seconds

It will take about 0.5 seconds more before the phone will hit the ground.

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Frequency of third harmonic is 122.48 HZ

Theory:

Frequency of third harmonic with length L , linear density μ , Tension

T is given as

                  fₙ= n v/2L

                   fₙ = n/2L × √T/√μ

      plugging in the values here-

                   fₙ =  3/ 2×0.5 × √50 / √0.03

                   fₙ = 122.48  Hz

          Thus, the frequency of third harmonic is 122.48 HZ

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Explanation:

Hello !

look at the attachment above ☝️ and if you have any questions your welcome.

a) The velocity after the collision.is 11.456 m/s.

b) The kinetic energy lost due to the collision is 44.564 J.

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. For inelastic collision, final velocity is the common velocity for both the bodies.

m₁u₁ +m₂u₂ =(m₁ +m₂) v

Given are the two objects, m1 = 0.6 kg and m2 = 4.4 kg undergo a one-dimensional head-on collision. Their initial velocities along the one-dimension path are vi1 = 32.4 m/s [right] and vi2 = 8.6 m/s [left].

(a) Substitute the values, then the final velocity will be

0.6 x32.4 +4.4 x 8.6 = (0.6+4.4)v

v = 11.456 m/s

Thus, the velocity after collision is 11.456 m/s.

(b) Kinetic energy lost due to collision will be the difference between the kinetic energy before and after collision.

= [1/2m₁u₁² +1/2m₂u₂² ] - [1/2(m₁ +m₂) v²]

Substitute the value, we have

= [1/2 x 0.6 x32.4² + 1/2 x4.4 x 8.6²] - [1/2 x(0.6+4.4)11.456²]

= 44.564 J

Thus, the kinetic energy lost due to the collision is 44.564 J.

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Uncertainty in position:

If the electron has an uncertainty in its velocity of 1.40 m/s then the uncertainty in its position is [tex]4.14\times10^{-4} \text{ m}[/tex].

Heisenberg's uncertainty principle to calculate the required:

Step-1:

We have to apply Heisenberg's uncertainty principle to calculate the uncertainty in the position of an electron. According to the principle:

[tex]$\Delta x \Delta p \geq \frac{h}{4 \pi}$[/tex]

Here,

[tex]$\Delta x$[/tex] is the uncertainty on the position measurement

[tex]$\Delta p$[/tex] is the uncertainty on the momentum measurement

h is the Planck constant.

It is known that the momentum of a particle is calculated as, the product of the mass of the particle and its velocity.

Therefore,

p=mv

Thus the Heisenberg principle becomes:

[tex]$m \Delta x \Delta v \geq \frac{h}{4 \pi}$[/tex]

Here [tex]$\Delta v$[/tex] is the uncertainty in the velocity measurement.

It is given that, [tex]$\Delta v$[/tex]=1.40 m/s. The particle is electron here, thus the mass of the particle m=[tex]9.1 \cdot 10^{-31} \mathrm{~kg}[/tex] and the value of the Plank's constant is, h=[tex]6.62 \times 10^{-34} \mathrm{~m}^{2} \mathrm{~kg} / \mathrm{s}[/tex]

Step-2:

Substituting the values into the equation to get the value of the position uncertainty.

[tex]\Delta x \geq \frac{h}{4 \pi\times m\times \Delta v}\\\geq\frac{6.62\times10^{-34}}{4\pi \times 9.1\times10^{-31}\times1.40} \text{ m}\\\geq 4.14\times10^{-4} \text{ m}[/tex]

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The answer is 73.13°.

According to snell's law,

n1sinθi = n2sinθr

n1/n2 = sinθr/sinθi

The critical angle is the angle of incidence at the denser medium when the angle of incidence at the less dense medium is 90°

This means i=C and r = 90°

The Snell's law formula will become

n1/n2 = sinC/sin90°

n2/n1 = 1/sinC

Where n1 is the refractive index of the less dense medium = 1.473

n2 is the refractive index of the denser medium = 1.540

Substituting the values in the formula,

1.540/1.473 = 1/sinC

1.045 = 1/sinC

SinC = 1/1.045

SinC = 0.957

C = sin^-1(0.957)

C = 73.13°

The refractive index of glass is 1.5. It way that the velocity of mild in glass is 1.5 times slower than the rate of mild in a vacuum, the speed of light in glass isn't always unbiased of the shade of mild.

Refractive index is likewise the same as the velocity of light c of a given wavelength in an empty area divided with the aid of its speed v in a substance or n = c/v.

The index of refraction of fabric is a ratio that compares the velocity of light in a vacuum ( c=3.00x108ms ) to the velocity of mild in that precise medium. Because the index of refraction increases, the amount that the material bends the mild increases.

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The critical angle (in degrees) for the light ray to remain inside the fiber is 73.13°.

According to snell's law,

n1sinθi = n2sinθr

n1/n2 = sinθr/sinθi

The critical angle is the angle of incidence at the denser medium when the angle of incidence at the less dense medium is 90°.

This means i=C and r = 90°

The Snell's law formula will become

n1/n2 = sinC/sin90°

n2/n1 = 1/sinC

Where n1 is the refractive index of the less dense medium = 1.473

n2 is the refractive index of the denser medium = 1.540

Substituting the values in the formula,

1.540/1.473 = 1/sinC

1.045 = 1/sinC

SinC = 1/1.045

SinC = 0.957

C = sin^-1(0.957)

C = 73.13°

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The time difference between their landing is 2.04 seconds.

The ball thrown vertical upwards will take double of the time taken by the ball thrown vertically downwards.

Time difference, = 2t - t = t

t = √(2h/g)

where;

Apply the principle of conservation of energy;

¹/₂mv² = mgh

h = v²/2g

where;

h = (20²)/(2 x 9.8)

h = 20.41 m

t = √(2 x 20.41 / 9.8)

t = 2.04 s

Thus, the time difference between their landing is 2.04 seconds.

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If the radio waves transmitted by a radio station have a frequency of 79.5 MHz, the wavelength of the waves, in meters is 3.77m.

Given: Velocity of light,  c = 3.00 x 10⁸ m/s  m/s

Frequency, f = 7.95 x 10⁷/s

For wavelength, the required formula is

[tex]λ = c/ f \\λ = 3 * 10 ^{8} / 7.95 * 10^{7} \\λ = 3.77[/tex]

Hence, the required wavelength is 3.77 meters.

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Constructive interference is the addition of wave energy as waves interact, producing larger waves and destructive interference is the subtraction of wave energy as waves interact, producing smaller waves.

To find the answer, we need to know about the interference of waves.

Thus, we can conclude that the constructive interference is the addition of wave energy and destructive interference is the subtraction of wave energy.

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Answer:

4.9 is the answer

Explanation:

pressure is force divided by area

force = mass x acceleration due to gravity

= 60kg x 9.8 m/s

area = length x width x height

=6 x 5 x 4

= 120

pressure = 588/120

= 4.9 pascal

The correct answer for the value of (i) Maximum pressure is [tex]24.5 \dfrac{N}{cm^2}[/tex](ii)Minimum pressure is [tex]19.6 \dfrac{N}{cm^2}[/tex].

Given:

Weight of the block:  [tex]60[/tex] kg

Dimensions of the box:  [tex]6 *4* 5[/tex]

Value of gravitational constant:  [tex]9.8[/tex] m/s²

Now,

[tex]Pressure = \dfrac{Force}{Area}[/tex]

[tex]Force = mass*accelaration[/tex]

[tex]= 60 * 9.8[/tex]

[tex]= 588 N[/tex]

Minimum pressure is when area is maximum:

[tex]= \dfrac{588}{6*5}\\\\= 19.6 \dfrac{N}{cm^2}[/tex]

Maximum pressure when area is minimum:

[tex]= \dfrac{588}{6*4} \\\\= 24.5 \dfrac{N}{cm^2}[/tex]

Maximum and minimum pressure are   [tex]24.5 \dfrac{N}{cm^2}[/tex]  and  [tex]19.6 \dfrac{N}{cm^2}[/tex] respectively.

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The value of the acceleration is 0.76 m/s² and the total time taken by the vehicle is 39 seconds.

The acceleration of the vehicle before coming to rest is calculated as follows;

v² = u² + 2as

where;

the car came to rest with constant velocity attained after 12 seconds.

the initial velocity of the car before 12 seconds is zero.

v² = 0 + 2as

a = v²/2s

a = (10²)/(2 x 66)

a = 0.76 m/s²

d = ut + ¹/₂at²

where;

580 = 0 + ¹/₂(0.76)t²

580 = 0.38t²

t² = 580/0.38

t² = 1,526.3

t = √1,526.3

t = 39 seconds

Thus, the value of the acceleration is 0.76 m/s² and the total time taken by the vehicle is 39 seconds.

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The reaction of the floor is as follows:

The reaction of the floor on the man is equal to the weight of the man and the upward force.

A)  When the lift moves upwards with steady speed.

R = 80 * 9.8 + * 80 * 0

R = 784 N

B) When the lift moves upwards with acceleration 0.4m/s

R = 80 * 9.8 + * 80 * 0.4

R = 816 N

In conclusion, the reaction of the floor changes as the body accelerates upwards.

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Answer:

Explanation:

Step 1

1 of 2

\textbf{Given}Given

n_{w}=1.33n

w

​

=1.33

$\theta_w=31\text{ ^\circ

∘

}$

$\theta_b=27\text{ ^\circ

∘

}$

\textbf{Approach}Approach

In this problem we are going to use Snell's law.

\textbf{Solution}Solution

The definition of Snell's law of refraction is

\begin{align} {n_1\cdot\sin \theta_1}={n_2\cdot \sin \theta_2} \end{align}

n

1

​

⋅sinθ

1

​

=n

2

​

⋅sinθ

2

​

​

​

where indexes 11 and 22 represent two different mediums. Since the motion is in the water we write

\begin{align} &{n_{w}\cdot\sin\theta_{w}}={n_{b}\cdot\sin\theta_{b}} \\ &{n_b}={n_{w}\cdot \frac{\sin\theta_{w}}{ \sin \theta_{b}} } \\ &{n_b}={1.33\cdot \frac{\sin31^\circ}{ \sin27^\circ} } \\ &\boxed{{n_b}=1.5} \end{align}

​

n

w

​

⋅sinθ

w

​

=n

b

​

⋅sinθ

b

​

n

b

​

=n

w

​

⋅

sinθ

b

​

sinθ

w

​

​

n

b

​

=1.33⋅

sin27

∘

sin31

∘

​

n

b

​

=1.5

​

​