A ball is thrown into the air with a velocity of 39 ft/s. Its height, in feet, after t seconds is given by s(t) = 39t − 16t2. Find the velocity (in ft/s) of the ball at time t = 1 second.

Answer:

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Use the work-energy theorem to find the velocity of the block when it's released by the spring. The work done by the spring on the block as it's restored to equilibrium is

W = 1/2 kx ²

where k is the spring constant and x is the compression of the spring. So

W = 1/2 (1400 N/m) (0.170 m)² = 20.23 J

This is equal to the block's change in kinetic energy ∆K,

W = ∆K

and since it starts from rest, the initial K is zero, leaving us with

W = 1/2 mv ²

where m is the mass of the block and v is its speed, so that

20.23 J = 1/2 (0.200 kg) v ²

==>   v ≈ 14.2 m/s

The block slides at this speed across the frictionless surface until it hits the incline which introduces friction.

First, you need to find the length of the incline. It forms a 45° angle, and the underlying 45°-45°-90° triangle has a hypotenuse of length √2 (2.0 m) ≈ 2.83 m.

Next, you need to find the total work done on the block as it slides up the incline. Use Newton's second law to examine the forces acting on the block during this phase:

• the net force acting on the block in the direction perpendicular to the incline is

∑ F = n - mg cos(45°) = 0

where n = mg cos(45°) ≈ 1.39 N is the magnitude of the normal force and mg cos(45°) ≈ 1.39 N is the perpendicular component of the block's weight;

• the net force acting on the block parallel to the surface is

∑ F = -f - mg sin(45°) = ma

where f = µn = 0.210n ≈ 0.291 N is the magnitude of kinetic friction, mg sin(45°) ≈ 1.39 N is the parallel component of the weight, and a is the acceleration of the block.

Only the parallel forces do work on the block, and this work is negative because friction and weight oppose the block's sliding up the incline. The total work done on the block is then

W = (-0.291 N - 1.39 N) (2.83 m) ≈ -4.74 J

Use the work-energy theorem again to find the block's new speed v at the top of the incline:

W = ∆K

==>   -4.74 J = 1/2 (0.200 kg) v ² - 1/2 (0.200 kg) (14.2 m/s)²

==>   v ≈ 12.4 m/s

And now this becomes a projectile problem. The block travels a horizontal distance x after being launched at an angle of 45° with initial speed 12.4 m/s after time t according to

x = (12.4 m/s) cos(45°) t

Its height y from the 2.0 m-high surface at time t is given by

y = (12.4 m/s) sin(45°) t - 1/2 gt ²

The block lands on the surface when y = 0, which occurs after t ≈ 1.79 s, at which point the block has covered a distance d ≈ 15.7 m.

The block sail through the air at the distance of "15.8 m"

Given:

Spring constant,

Mass,

Block's coefficient,

By using Work energy theorem, we get

→ [tex]W_{spring}+W_g+W_f = KE_f-KE_i[/tex]

By substituting the values, we get

→ [tex]\frac{1}{2}\times 1400\times (0.17)^2- (0.2\times 9.8\times 2)-(0.21\times 0.2\times \frac{9.8}{\sqrt{2} }\times \sqrt{2}\times 2 )= \frac{1}{2}\times 0.2\times V_f^2[/tex]

here,

[tex]V_f = 12.44 \ m/s[/tex]

→ [tex]d = \frac{V_f^2 Sin 2 \Theta}{g}[/tex]

     [tex]= \frac{(12.44)^2 Sin 90^{\circ}}{9.8}[/tex]

     [tex]= 15.8 \ m[/tex]

Thus the answer above is right.  

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Answer:

Explanation:

The mass of that science book...wow. In pounds that would be 35.2! Yikes!

Anyway, we need final velocity here, and the mass of the book has nothing to do with how fast it falls. Everything is pulled by the same gravity. A feather falls at 9.8 m/s/s and so does an elephant. Mass is useless information. The equation we will use is

[tex]v^2=v_0^2+2a[/tex]Δx  where

v is the final velocity, our unknown,

v₀ is the initial velocity which is 0 since someone had to be holding the book before dropping it,

a is the pull of gravity which is always -9.8 m/s/s, and

Δx = -120 which is the displacement (it's negative because the book falls below the point from which it was dropped). Filling in:

[tex]v^2=0^2+2(-9.8)(-120)[/tex] so

[tex]v=\sqrt{2(-9.8)(-120)}[/tex] and

v = 48 m/s

As far as how far above the bottom of the cliff the object is when it is moving at 12 m/s we will use the same equation, but the velocity will be 12:

[tex]12^2=0^2+2(-9.8)[/tex]Δx and

144 = -19.6Δx so

Δx = -7.3 m. That's how far from the top of the cliff it is. We subtract then t find out how far it is from the bottom:

120 - 7.3 = 112.7 m off the ground.

Two things are said to be in contact if the smallest distance between a point in one of them and a point in the other one is zero.

Answer:

kinetic

Explanation:

i just remember it from last year

Answer:

kinetic energy

Explanation:

expression for kinetic energy is

kinetic energy = (1/2) × mass × (velocity)^2

so , as velocity increases K.E increases

Answer:

The work done is -209.42 J.

Explanation:

F(x) = (- 20 - 3 x ) N

x = 0 to x = 6.9 m

Here, the force is variable in nature, so the work done by the variable force is given by

[tex]W =\int F dx\\\\W =\int_{0}^{6.9}(-20- 3x dx )\\\\W= \left [ - 20 x - 1.5 x^2 \right ]_{0}^{6.9}\\\\W = - 20 (6.9 - 0) - 1.5(6.9\times 6.9 - 0)\\\\W =- 138 - 71.42\\\\W = - 209.42 J[/tex]

Answer:

Length = 3.136 meters

Explanation:

Given the following data;

Speed = 345 m/s

Frequency = 440 Hz

To find how long is the tube;

First of all, we would determine the wavelength;

Wavelength = speed/frequency

Wavelength = 345/440

Wavelength = 0.784 m

Next, we would determine how long is the tube using the formula;

[tex] Length = \frac {2n - 1}{4} * wavelength [/tex]

Substituting into the formula, we have;

[tex] Length = \frac {2*1 - 1}{4} * 0.784 [/tex]

[tex] Length = \frac {2 - 1}{4} * 0.784 [/tex]

[tex] Length = \frac {1}{4} * 0.784 [/tex]

Length = 3.136 meters

Answer:

The speed of projection is 34 m/s.

Explanation:

Height of building, h = 51 m

horizontal distance, d = 74 m

time, t = 8 s

Let the angle is A and the speed is u.

d = u cos A x t

74 = u cos A x 8

u cos A = 9.25 .... (1)

Use second equation of motion

[tex]h = u sin A t - 0.5 gt^2\\\\-51 = u sinA \times 8 - 0.5\times 9.8\times8\times 8\\\\u sin A = 32.8 .... (2)[/tex]

Squaring and adding both the equations

[tex]u^2 = 9.25^2 + 32.8^2 \\\\u = 34 m/s[/tex]

Answer:

you can use G.oogle for this question.

Answer:

93.3 degrees Celsius.

Explanation:

Answer:

The answer is below

Explanation:

The intensity level (B) of a sound wave is given by:

B = 10log(I/I₀);

where I₀ is the threshold intensity = 1 * 10⁻¹² W/m², I is the intensity at distance 5 m, B is the intensity level = 52 dB

Substituting gives:

[tex]52=10log(\frac{I}{10^{-12}} )\\\\log(\frac{I}{10^{-12}} )=5.2\\\\I=1.58*10^{-7}\ W/m^2[/tex]

The pressure is given by:

[tex]I=\frac{p_{max}^2}{2\rho v} \\\\\rho=air\ density=1.2\ kg/m^3,v=speed\ of\ sound\ in\ air=344\ m/s,p_{max}=pressure:\\\\p_{max}=\sqrt{2\rho vI}=\sqrt{2*1.58*10^{-7}*1.2*344} =1.14*10^{-2}Pa[/tex]

Answer:

Penetration means forward passes can go through the opposition lines. Once these penetrative passes get through each line, it eliminates the line of players it broke through and leaves the player in possession closer to the opposition goal.

Explanation:

Answer:

[tex]w_2=38.3rpm[/tex]

Explanation:

From the question we are told that:

Mass of turntable [tex]M=2.2kg[/tex]

Diameter of turntable [tex]d=20cm=>0.2m[/tex]

Angular Velocity [tex]\omega =80rpm[/tex]

Mass of Blocks [tex]M_b=600g=>0.6kg[/tex]

Generally the equation for inertia is mathematically given by

Initial scenario at \omega=80rpm

 [tex]I_1=\frac{1}{2}mR^2[/tex]

 [tex]I_1=\frac{1}{2}*2.2*0.1^2[/tex]

 [tex]I_1=0.11kgm^2[/tex]

Final scenario

 [tex]I_2=I_1+2mR^2[/tex]

 [tex]I_2=0.011+(2*0.6*0.12)[/tex]

 [tex]I_2=0.023[/tex]

Generally the equation for The relationship between Angular velocity and inertia is mathematically given by

 [tex]I_1w_1=I_2w_2[/tex]

 [tex]w_2=\frac{I_1 \omega}{I_2}[/tex]

 [tex]w_2=\frac{0.011*80}{0.023}[/tex]

 [tex]w_2=38.3rpm[/tex]

Answer:

Decrease occur in kinetic energy.

Explanation:

The kinetic energy decreases when the the Bob swings reaches to the maximum height because the motion of the bob slower down. At maximum height, the kinetic energy decreases whereas the value of potential energy is the highest. The main reason of higher potential energy is that it depends on height of an object while on the other hand, kinetic energy depends on the motion of an object so that's why the value of kinetic energy decreases and potential energy increases at maximum height of the bob.

Answer:

First of all the formula is F= uR,( force= static friction× reaction)

mass= 5+25=30

F= 50

R= mg(30×10)=300

u= ?

F=UR

u= F/R

u= 50/300=0.17N

Answer:

False.

Explanation:

Suppose that we have an object that moves with constant acceleration A.

Then the acceleration of the object is defined by the equation:

a(t) = A

The acceleration is the rate of change of the velocity, then the velocity equation is given by the integration of the acceleration equation, we will get:

v(t) = A*t + V₀

Where V₀ is the velocity of the object at the time t = 0s.

Now, if we integrate it again, we will get the position equation:

p(t) = (1/2)*A*t^2 + V₀*t + P₀

Where P₀ is the initial position equation.

Here, we can see that the position equation is a quadratic equation (not a linear equation), then the statement is false.

The correct answer is option B. Determine whether experimental observations can provide evidence to support a conclusion.

1. Identify the research question: Begin by clearly defining the question or problem that you want to investigate. This question should be specific and focused, allowing for clear hypotheses to be developed.

2. Conduct background research: Familiarize yourself with existing knowledge and previous research related to your question. This step will help you understand the current state of knowledge in the field and identify any gaps or areas that require further investigation.

3. Formulate a hypothesis: Based on your background research, develop a hypothesis that proposes a possible explanation or answer to your research question. A hypothesis should be a clear statement that can be tested through experimentation or observation. It should be specific, measurable, and falsifiable, meaning that it can be proven wrong if the evidence does not support it.

4. Design experiments or observations: Once you have formulated a hypothesis, consider the experimental or observational methods that can be used to test it. Determine what data you need to collect, what variables you need to manipulate or measure, and what controls should be put in place to ensure the validity of your results.

5. Predict outcomes: Based on your hypothesis, make predictions about the expected outcomes of your experiments or observations. These predictions should be derived from your hypothesis and should be specific enough to be tested.

6. Conduct the experiment or observation: Carry out the planned experiments or observations, ensuring that you collect and record data accurately. Implement proper controls and procedures to minimize any biases or confounding factors that could affect the results.

7. Analyze the data: Once you have collected the data, analyze it using appropriate statistical or analytical methods. Evaluate whether the data supports or contradicts your hypothesis and predictions.

8. Draw conclusions: Based on the analysis of your data, draw conclusions about whether the evidence supports or refutes your hypothesis. Clearly state the findings and discuss their implications in the context of the research question.

9. Communicate the results: Share your findings with the scientific community through scientific papers, presentations, or other appropriate means. Allow other scientists to review and replicate your work, fostering further discussion and advancement in the field.

Remember, the scientific process is iterative, and developing a hypothesis is just the starting point. Scientists continuously refine and revise their hypotheses based on new evidence and insights gained from their experiments and observations.

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Answer:

The right solution is "4.8° east of north".

Explanation:

Given:

Distance,

= 500 km

Speed,

[tex]\vec{v}=120 \ m/s[/tex]

Wind (towards west),

[tex]v_0=10 \ m/s[/tex]

According to the question, we get

The angle will be:

⇒ [tex]\Theta=Cos^{-1}(\frac{v_0}{v_1} )[/tex]

       [tex]=Cos^{-1}(\frac{10}{120} )[/tex]

       [tex]=85.21[/tex] (north of east)

hence,

The direction must be:

⇒ [tex]\Theta'=90-85.21[/tex]

        [tex]=4.79^{\circ}[/tex]

or,

        [tex]=4.8^{\circ}[/tex] (east of north)

Answer:

Example:Opening of a bottle cap by tool

when we hold a tool and open the bottle cap this is because , force x tool force .

The load arm is usually shorter than the effort arm in second order levers. Moving a large weight hence requires less effort. A force multiplier lever or effort multiplier lever is the name for this kind of lever. A boat's oars, for instance, can increase the force.

Second-order levers are devices with the input force farthest from the fulcrum and the output force on the same side of the fulcrum. A wheelbarrow is an excellent illustration of a second-order lever.

A second-order lever will have an output force greater than an input force, similar to first-order levers. The output journey, however, will be shorter than the input length. Both the input and output forces in this situation will move in the same direction.

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Answer:

C) 40m/s [R]

Explanation:

Given the following data;

Force = 25 N [L]

Mass = 1 kg

Initial velocity = 0 m/s

Velocity = 10 m/s [R]

Time = 2 seconds

To find the final velocity;

First of all, we would determine the acceleration of the object.

Force = mass * acceleration

25 = 1 * acceleration

Acceleration = 25/1

Acceleration = 25 m/s²

Next, we would determine the final velocity by using the first equation of motion;

[tex] V = U + at[/tex]

Where;

V is the final velocity.

U is the initial velocity.

a is the acceleration.

t is the time measured in seconds.

Substituting into the formula, we have;

[tex] V = 0 + 25*2[/tex]

[tex] V = 0 + 50 [/tex]

V = 50 m/s

Final velocity = 50 - 10

Final velocity = 40 m/s [R]

Answer:

(a) v₁ = 51.96 km/h

(b) v₁ = 178 km/h

Explanation:

(a)

For having the same momentum:

m₁v₁ = m₂v₂

where,

m₁ = mass of Volkswagen = 816 kg

v₁ = speed of Volkswagen = ?

m₂ = mass of Cadillac = 2650 kg

v₂ = speed of Cadillac = 16 km/h

Therefore, using these values in the equation, we get:

[tex](816\ kg)v_1 = (2650\ kg)(16\ km/h)\\\\v_1 = (16\ km/h)(\frac{2650\ kg}{816\ kg})[/tex]

v₁ = 51.96 km/h

(b)

For having the same momentum:

m₁v₁ = m₂v₂

where,

m₁ = mass of Volkswagen = 816 kg

v₁ = speed of Volkswagen = ?

m₂ = mass of Truck = 9080 kg

v₂ = speed of Truck = 16 km/h

Therefore, using these values in the equation, we get:

[tex](816\ kg)v_1 = (9080\ kg)(16\ km/h)\\\\v_1 = (16\ km/h)(\frac{9080\ kg}{816\ kg})[/tex]

v₁ = 178 km/h

Answer:

We know that the change in electric potential energy is defined as:

q*ΔV = ΔP

So, the change in the electric potential energy is the charge times the change in the electric potential.

For the case of an electron gas, we have:

q = -e

where -e is the charge of an electron (remember that is negative).

So, if the electron gains electric potential then:

ΔP > 0

this means that the final potential energy is larger than the initial one, then we have:

-e*ΔV > 0

This means that ΔV must be negative.

V₂ = electric potential at point 2, so it is the final electric potential

V₁ = electric potential at point 1, so it is the final electric potential

Then we should get:

ΔV = V₂ - V₁ < 0.

This means that:

V₂ < V₁

The correct option is b.

Answer:

Angle of reflection

Explanation:

The angle between the reflected ray and the normal line is called the angle of reflection

Answer:

Activity 2 Directions: Solve the following problems using Charles' Law,

1. A 3.8 mL of a gas in a container has a temperature of 2.0K. What would the volume be if the temperature becomes 8.0K?

2. If at 27°C the volume of a dry gas is 3.0 ml. What is the new temperature if the volume increased to 7.5 ml?

3. The temperature of the gas is 460,0 mL at 3.5°C. Calculate the new volume at 1.5°C

Answer:

[b] it id heated from 4o

Explanation:

Answer:

[tex]F = 14.2 N[/tex]  

Explanation:

From the question we are told that:

Mass [tex]m=0.15kg[/tex]

Radius [tex]r=0.6[/tex]

Angular Velocity [tex]\omega=2rev/s[/tex]

                            [tex]\omega= =2x2 \pi rad/s=>4 \pi rad/s[/tex]

Generally the equation for Force applied is mathematically given by

 [tex]F =mrw2[/tex]

 [tex]F=0.15*0.6* (4*x3.14^)2[/tex]

 [tex]F = 14.2 N[/tex]    

Answer:

Flux is 21 Nm^2/C.

Explanation:

Electric field, E = 6 N/C along X axis

Electric filed vector, E = 6 i N/C

Area, A = 4 square meter

Area vector

[tex]\overrightarrow{A} = 4 (cos30 \widehat{i} + sin 30 \widehat{j})\\\\\overrightarrow{A} = 3.5 \widehat{i} + 2 \widehat{j}\\[/tex]

The flux is given by

[tex]\phi= \overrightarrow{E}.\overrightarrow{A}\\\\\phi = 6 \widehat{i} . \left (3.5 \widehat{i} + 2 \widehat{j} \right )\\\\\phi = 21 Nm^2/C[/tex]

Answer:

(a) 81.54 N

(b) 570.75 J

(c) - 570.75 J

(d) 0 J, 0 J

(e) 0 J  

Explanation:

mass of crate, m = 32 kg

distance, s = 7 m

coefficient of friction = 0.26

(a) As it is moving with constant velocity so the force applied is equal to the friction force.

F = 0.26 x m x g = 0.26 x 32 x 9.8 = 81.54 N

(b) The work done on the crate

W = F x s = 81.54 x 7 = 570.75 J

(c) Work done by the friction

W' = - W = - 570.75 J

(d) Work done by the normal force

W'' = m g cos 90 = 0 J

Work done by the gravity

Wg = m g cos 90 = 0 J

(e) The total work done is

Wnet = W + W' + W'' + Wg = 570.75 - 570.75 + 0 = 0 J  

Answer:

both swings at the same place

Explanation:

because there mother is giving same amount of force to both.