The image formed is 0.25 times the size of the object and 10 cm behind the pinhole. If the height of image on screen is 6 cm what is the distance of the object from the screen?

Answer:

The x - intercept is 1/3

The y - intercept is 1/2

The gradient is -3/2

Explanation:

To find the x - intercept of the equation 2y + 3x = 1, we find the value of x when y = 0. So,

2y + 3x = 1

2(0) + 3x = 1

0 + 3x = 1

3x = 1

x = 1/3

So, the x - intercept is 1/3

To find the y - intercept of the equation 2y + 3x = 1, we find the value of y when x = 0. So,

2y + 3x = 1

2y + 3(0) = 1

2y + 0 = 1

2y = 1

y = 1/2

So, the y - intercept is 1/2

To find the gradient of the equation 2y + 3x = 1, we re-write it in gradient intercept form by making y subject of the formula.

So, 2y + 3x = 1

2y = -3x + 1

y = -3x/2 + 1/2

The coefficient of x which equals -3/2 is the gradient.

The gradient is -3/2

Answer:

The maximum induced emf is 15.08 V

Explanation:

Given;

number of turns of the generator, N = 6 turns

area of the loop, A = 0.04 m

magnetic field of the loop, B = 0.2 T

frequency of loop, f = 50 Hz

The  maximum induced emf is given by;

E = NBAω

Where;

ω is the angular speed = 2πf

E = NBA(2πf)

E = 6 x 0.2 x 0.04 x (2 x 3.142 x 50)

E = 15.08 V

Therefore, the maximum induced emf is 15.08 V

Answer:

22.73 m/s or 81.72 kph

Explanation

We can find the combined mass of both cars as

970 kg + 2300 kg = 3270 kg.

Then the normal force of the cars can be calculated as

F(n)= mg

Where g is acceleration due to gravity 9.8m/s^2

3270 kg ×9.8 = 32046 kg*m/s^2.

coefficient of kinetic friction between tires and road to be 0.80 × F(n)

Then the frictional force can be calculated as

= (32046kg*m/s^2 × 0.80 )

= 25636.8 kg*m/s^2

We can now calculate the work done that was used stopping the cars as

Frictional force × distance

(25636.8 kg*m/s^2 ) × 2.9m= 74346.72kg*m^2/s^2

From kinetic energy formula, the combined velocity of the car can be determined

E=0.5 M V²

√(2E/M) = V

√(2*74346.72kg*m^2/s^2 / 3270 kg) = V

V= √ (45.472)

V=6.743293m/s

the momentum of both cars can be determined as

6.743293m/s * 3270 kg

= 22050.57kg*m/s

Now the final momentum of both cars must be equal to the the momentum of

the sports car just prior to the collision. Therefore, the speed of the sports car at impact.

=(22050.57 kg*m/s) / 970 kg = 22.73 m/s

We can convert that to km/h.

22.73 m/s * 3600 s/h / 1000 m/km = 81.72 kph

Answer:

The answer is either 47 or 23. Most likely 47

Explanation:

nitrogen fixation is the process by which nitrogen gas form the atmosphere is converted into different compound that can be used by plants and animal. there are three major ways in which this happens: first, by lightning, second by industrial methods and finally by bacteria living in the soil.

Answer:

9 kg

Explanation:

Momentum is mass times velocity.

p = mv

36 kgm/s = m (4 m/s)

m = 9 kg

The mass of the bicycle is 9 kg.

The momentum of the bicycle is the product of mass and velocity of the bicycle.

P = mv

where;

m = P/v

m = 36/4

m = 9 kg

Thus, the mass of the bicycle is 9 kg.

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Answer:

the rock will sink. this is because it is more dense than water

Answer:it will sink

Explanation:

because the density of water is 1g and the rock is heavier the the density of water

Answer:

230 = x + 105

x= 125

Explanation:

v = v0 + at

Answer:

12.5 m/s

Explanation:

a = Δv / Δt

2.5 m/s² = Δv / 5 s

Δv = 12.5 m/s

Answer:

i) 60 W

ii) 100 W

Explanation:

In each case, the bulb that dissipates the most power is the bulb that glows brighter.  Power is voltage times current (P = VI).  Using Ohm's law, we can rewrite this as P = I²R or P = V²/R.

Bulbs are rated at a certain power for a certain voltage.  P = V²/R, so the bulb with the lower resistance will have the higher power rating.  Therefore, the 100 W bulb has a lower resistance than the 60 W bulb.

i) They are in series, so they have the same current.  P = I²R, so the bulb with the higher resistance will glow brighter.  That's the 60 W bulb.

ii) They are in parallel, so they have the same voltage.  P = V²/R, so the bulb with the lower resistance will glow brighter.  That's the 100 W bulb.

Answer:

As rocket mass increases, acceleration decreases.

Explanation:

From Newton's second law of motion;

F= ma

Where;

m= mass of the object

a= acceleration of the object

Hence we can write;

a= F/m

This implies that an increase in mass (m) will lead to a decrease in acceleration if the force on the object is held constant.

Hence, if the rockets have different masses, they will have different accelerations.

Hello!

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As rocket mass increases, acceleration decreases.

Hope this helps! The rest are available on Quizlet at "Unit 6: Lesson 4 Force, Mass and Acceleration". Thanks and good luck!

Answer:

Answer:

The answer  is The acceleration is double its original value.

Explanation:

Hope this helps....

Have a nice day!!!!

Answer:

The acceleration is half of its original value

Explanation:

Answer:

The distance traveled by the ball is 8.5 m

Explanation:

Initial height of the ball, h₁ = 1.5 m above the ground

final height of the ball, h₂ = 5m

Upward distance = distance traveled by the ball from a height of 1.5m to 5m = 5m - 1.5m = 3.5 m

Downward distance = distance traveled by the ball from 5m height to the ground =5m - 0 = 5m

Total distance traveled = upward distance + downward distance

Total distance traveled = 3.5 m + 5m = 8.5 m

Therefore, the distance traveled by the ball is 8.5 m

Answer:

1) The balloon will shrink

2) The balloon will grow bigger and regain its shape

Explanation:

By the kinetic theory of gases, we have;

[tex]v_{rms} = \sqrt{\dfrac{3 \cdot R \cdot T}{MW} }[/tex]

[tex]P = \dfrac{n \cdot MW \cdot vrms^2}{3 \cdot V}[/tex]

Where;

[tex]v_{rms}[/tex] = RMS Speed

R = The universal gas constant

T = The temperature

MW = The Molecular weight

n = The number of moles

V = The volume

P = The pressure

1) When the balloon is placed in the refrigerator for  minutes, the temperature inside the balloon will drop and RMS speed will reduce, however due to the elastic wall of the balloon, the pressure will remain the same therefore the volume  will reduce and the balloon will shrink

2) When the balloon is placed on the kitchen counter, the temperature inside the balloon will rise leading to the increase in the RMS speed which will raise the pressure effect on the wall  of the balloon as the balloon is made of elastic material, as the pressure rises, the wall expands to keep the pressure constant and the volume occupied by the air particles will increase, the balloon will grow bigger and regain its shape.

Answer:

=33 .3×10^6Ω

=33.3M Ω

Explanation:

We were told to calculate the Resistance value,

Given the heart pacemaker fires as 72 times a minute, which is the time constant

Then we can convert the pacemaker fires of 72 times a minute to seconds for unit consistency.

1 minutes= 60secs

Then ,Time constant τ=60secs/72=0.8333 seconds

Time constant τ can be calculated using the formula below

τ= RC

Where R= resistance

C = capacitance

Then making RESISTANCE subject of formula we have

R=τ/C

But Capacitance=25.0-nF = 25×10^25F

Substitute the values we have

R=0.833/25×10^25

=33 .3×10^6 Ω

But can still be converted to M Ω= 33.3M Ω

Therefore, the resistance is 33 .3×10^6 Ω or 33.3M Ω

NOTE: 1M= 10^6

The value of the resistance will be "3.33×10⁷ Ω".

According to the question,

Capacitor, C = 25.0 nF

60 sec - 72 fires

now,

Time for 1 fire,

[tex]t = \frac{60}{72}[/tex]

 [tex]= \frac{5}{6} \ sec[/tex]

Now,

⇒            [tex]V = V_0 (1-e^{-\frac{t}{RC} })[/tex]

     [tex]0.632 V_0=V_0(1-e^{\frac{-\frac{5}{6} }{R.25 n C} })[/tex]

[tex]e^{-\frac{1}{R\times 30\times 10^{-9}} } = 1-0.632 = 0.368[/tex]

                  [tex]= 2.72[/tex]

By taking "log" both sides,

⇒ [tex]ln \ e^{\frac{1}{R\times 30\times 10^{-9}} } = ln \ 2.72[/tex]

hence,

The Resistance be:

⇒ [tex]R = \frac{10^9}{30}[/tex]

       [tex]= 3.33\times 10^7 \ \Omega[/tex]

Thus the above approach is right.

Find out more information about resistance here:

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Answer:

Upthrust = 20 N

Explanation:

The question says that "A body weighs 100N in air and 80N when submerged in water. Calculate the upthrust acting on the body ?"

Upthrust is defined as the force when a body is submerged in liquid, then liquid applies a force on it.

ATQ,

Weight of body in air is 100 N

Weight of body in water is 80 N

Upthrust is equal to the weight of body in air minus weight of body in water.

Upthrust = 100 N - 80 N

Upthrust = 20 N

So, 20 N of upthrust is acting on the body.

Answer:

D=M/V. That's the formula. Density is expressed, in cubic centimeters.

Explanation:

Answer:g/m³

g/cm³

-kg/L

-kg/cm³

Density in physics, is defined as the mass of the object over its volume. Density is considered as how much matter is contained in a single object by its volume or the matter that it occupies.

D = m / v

Explanation:

Answer:

Answer B is the correct answer: "Motion of one projectile as seen from the other is a straight line."

Explanation:

Let's write the equations of motion for each projectile, using that projectile [tex]a[/tex] is launched with velocity [tex]a[/tex] which has components associated with the angle of launching, given in x and y coordinates as: [tex]a_x\,\,and\,\,a_y[/tex].

Similarly, assume that projectile b is launched with velocity [tex]b[/tex] with components due to the launching angle = [tex]b_x\,\,and \,\,b_y[/tex]

then the equations of motion for the two projectiles launched at the same time (t) from the same spot (position that we assume to be at the origin of coordinates to simplify formulas) are:

[tex]x_a=a_x\,t\\y_a= a_y\,t-\frac{1}{2} g\,t^2\\and\\x_b=b_x\,t\\y_b= b_y\,t-\frac{1}{2} g\,t^2[/tex]

therefore, from the frame of reference of projectile "b", the x and y position of projectile "[tex]a[/tex]" would be:

[tex]x_{a\,b}= x_a-x_b= a_x\,t-b_x\,t=(a_x-b_x)\,t[/tex]  which is linear in "t"

[tex]y_{a\,\,b}=y_a-y_b= a_y\,t-\frac{1}{2} g\,t^2-\left[ b_y\,t-\frac{1}{2} g\,t^2\right]=(a_y-b_y)\,t[/tex] which is also linear in t.

Therefore the motion of one projectile with reference to the other is a straight line (answer B)

Notice as well that this two projectiles cannot collide because they have been launched together, and supposedly at different speeds and angles. The only way that they can share the same x-coordinate and the same y-coordinate at the same time "t" is if their velocity components are equal, which is not what we are told.

[tex]x_a=x_b\\a_x\,t= b_x\,t\\and\\y_a= y_b\\a_y\,t-\frac{1}{2} g\,t^2= b_y\,t-\frac{1}{2} g\,t^2\\a_y\,t=b_y\,t\\a_y=b_y[/tex]

Answer:

The pressure at the bottom of the river is less than that at the bottom of the lake.

Explanation:

From Bernoulli's equation, the pressure difference is given by

ΔP = ρgΔh + ρ(v₂² - v₁²)/2 where ρ = density of water, g = acceleration due to gravity, Δh = depth, v₁ = velocity at top, v₂ = velocity at bottom

For the lake, v₁ = v₂, since the velocity at the top and bottom are the same. So,

ΔP₁ = ρgΔh + ρ(v₁² - v₁²)/2 = ρgΔh + 0 = ρgΔh

P₂ - P₁ = ρgΔh

P₂ = P₁ + ρgΔh

For the river, v₁ < v₂, since the velocity at the top of the river is greater than at the bottom.

So,

ΔP₂ = ρgΔh + ρ(v₂² - v₁²)/2.

Since  v₁ < v₂, ρ(v₂² - v₁²)/2 will be negative,

So,

ΔP₂ = ρgΔh - ρ(v₂² - v₁²)/2.

Since ρ(v₂² - v₁²)/2 is negative, making ΔP less than that in the lake.

So, ΔP₂ = ΔP₁ -  ρ(v₂² - v₁²)/2.

ΔP₂ = P₃ - P₁

P₃ - P₁ = P₂ - P₁ -  ρ(v₂² - v₁²)/2.

P₃ = P₂ - ρ(v₂² - v₁²)/2.

where P₃ = pressure at bottom of the river and P₂ = pressure at bottom of the lake and P₁ = atmospheric pressure at top of river and lake respectively.

Since the factor ρ(v₂² - v₁²)/2 is removed from the pressure at the bottom of the lake, the pressure at the bottom of the river is therefore less than that at the bottom of the lake.

Answer:

The linear velocity of europe's motion in its orbit is 7875.58 km/hr.

Explanation:

Given that,

Time period of lo = 1.77 days

Time period of europa = 3.55 days

Distance of lo from jupiter = 421600 km

We know that,

Distance of europa from jupiter = 671000 km

We need to calculate the linear velocity of europe's motion in its orbit

Using formula of velocity

[tex]v=\dfrac{d}{t}[/tex]

Where, d = distance between europa and jupiter

t = time

Put the value into the formula

[tex]v=\dfrac{671000}{3.55\times24}[/tex]

[tex]v=7875.58\ km/hr[/tex]

Hence, The linear velocity of europe's motion in its orbit is 7875.58 km/hr.

1. Which example best describes a restoring force?

B) the force applied to restore a spring to its original length

2. A spring is compressed, resulting in its displacement to the right. What happens to the spring when it is released?

C) The spring exerts a restoring force to the left and returns to its equilibrium position.

3. A 2-N force is applied to a spring, and there is displacement of 0.4 m. How much would the spring be displaced if a 5-N force was applied?

D) 1 m

4. Hooke’s law is described mathematically using the formula Fsp=−kx. Which statement is correct about the spring force, Fsp?

D)It is a vector quantity.

5. What happens to the displacement vector when the spring constant has a higher value and the applied force remains constant?

A) It decreases in magnatude.

Answer:

The distance of the light is 9.4608 x 10^25 m

Explanation:

Time taken by the light = 10 billion years = 10 x 10^9 years

speed of light = 3 x 10^8 m/s

speed of light in m/years is = (3 x 10^8)/(60 x 60 x 24 x 365) = 9.4608 x 10^15 m/year

distance = speed x time

therefore, the distance of this light = 10 x 10^9 x 9.461 x 10^15 = 9.4608 x 10^25 m

Answer:  

more than 10 billion light years due to expansion of space

Explanation:

Answer:Adolescent chastity can be defined as the absolute abstinence from sex and anything related to sex, such as, kissing, touching, fondling

Explanation:

Explanation:

Use Pythagorean theorem:

r² = x² + y²

r² = (-7.11 m)² + (-4.41 m)²

r = 8.37 m

Use trig to find the angle.

tan θ = y / x

tan θ = (-4.41 m) / (-7.11 m)

θ = 31.8° or 211.8°

Since x is negative and y is negative, the point is in the third quadrant, so θ = 211.8°.

Or, if we subtract 360°, θ = -148.2°.

Answer:

is a force that attracts any two objects with a mass

Answer:

“They may feel colder but that's only an illusion,” Dr. Begley says. “Copper mugs actually absorb heat from the room faster than a glass.” Copper is an excellent thermal conductor, meaning it transfers heat from hot sources (like the room or your hand) to cold sources (like your drink) very efficiently.

Explanation:

Answer:

12 i. The work done by Wale = 107.910 kJ

The work done by Lekan = 117.720 kJ

Total work done = 225.36 kJ

ii. Wale's power =  4.3164 kW

Lekan's power = 3.924 kW

Wale has more power and is more powerful than Lekan

13. 313.92 N

Explanation:

i. The work done, W = Force, F × Distance moved by the force, D

The given parameters are

The mass of Wale = 55 kg

The mass of Lekan = 60 kg

The acceleration due to gravity, g =9.81 m/s²

The motion force of Wale and Lekan are;

Motion force of Wale = 9.81 × 55 = 539.55 N

Motion force of Lekan = 9.81 × 60 = 588.6 N

The work done by Wale = 539.55 × 200 = 107910 J = 107.910 kJ

The work done by Lekan= 588.6 × 200 = 117720 J = 117.720 kJ

107910 + 117720 =225630 J = 225.36 kJ

ii. Power = Work done/time

Wale finished the race in 25 s, therefore, his power = 107910/25 = 4316.4 W

Lekan finished the race in 30 s, therefore, his power = 117720/30 = 3924 W

Wale has more power and is more powerful than Lekan

13. The velocity ratio = 5

V. R. = Distance moved by effort/(Distance moved by load)

Efficiency = 80%

Work done by effort = x

Work done by machine = Efficiency × Work done by effort  = 0.8 × x

Distance moved by effort, E = V. R. × Distance moved by load, D = 5 × D

Work done by effort = Force × Distance moved = 200×9.81× E

Work done by effort = 1962×E = 1962×E = 1962×5×D

Work done by machine = 1962 × D, when D = 1, we have;

0.8 × 1962×1 = 1569.6 J

Work done by effort = Force × Distance moved

Work done by effort = Force × 5×D = Force × 5 (D = 1)

From the principle of conservation of energy, we have;

Energy is neither created nor destroyed

Therefore

Work done by effort = Force × 5 = 1569.6 J

Force = 1569.6 /5 = 313.92 N.

Answer:

hypernova making a black hole, and merger of two neutron stars