A cannon is fired horizontally from the top of a platform, with a velocity of 18m/s. If the cannon ball
lands 162m away from the base of the platform, How long does it take for the cannon ball to hit the
ground? How tall is the platform?
I

From the given data,

Part A: -In opposite direction Greatest impulse B>C>A>D>E smallest impulse

Part B: -increasing constantly thus acceleration is increasing resulting in increase of velocity and momentum as well.

Part C: -\(Force $=m$ a $\) =\($m \frac{\Delta v}{\Delta t}=\) \(m$ momentum\)

       \(F=\frac{m}{\Delta t}\)

Mass of box  \(=10kg\)

Impulse = \(F_{average}\) At

A. 0-2 seconds

Impulse = 1.5×2 = 3N sec

B. 2-4 sec

Impulse = 3×2 = 6N sec

C. 4-6 sec

Impulse = 2.75×2 =5.5N sec

D. 6-8 sec

Impulse = 1×2 = 2N sec

E. 8-10 sec

Impulse = 1×2 = 2N sec

In opposite direction Greatest impulse B>C>A>D>E smallest impulse.

For the first two seconds force is increasing constantly thus acceleration is increasing resulting in increase of velocity and momentum as well. Now for the next three seconds a constant force is acting on the box resulting in constant acceleration. After that for the next three seconds force goes on decreasing constantly thus deacceleration and decrease of impulse and velocity. In last 2 seconds deacceleration is in opposite direction that is how box starts moving in opposite direction

\((1) Force $=m$ a $\)\($=m \frac{\Delta v}{\Delta t}=\)\(m$ momentum\)

             \(F=\frac{m}{\Delta t}\)

(2) Area under the curve gives the momentum

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Answer:

amount and speed of traffic on the acceleration lane and expressway.

Answer:

1700 Joules

Explanation:

Work=force x distance

Force = 170 kg

Distance= 10 Meters

170 x 10 = 1700 Joules of work

To calculate the value of the capacitor for tuning to the 1020 kHz radio station, we can use the formula for resonant frequency:

f = 1 / (2 * π * √(LC))

Rearranging the formula to solve for capacitance (C), we get:

C = 1 / (4 * π² * f² * L)

Substituting the given values of frequency (1020 kHz) and inductance (70 μH), we can calculate the capacitance to be tuned as approximately 118.7 pF.

To find the peak current at resonance, we can use the formula for the peak current (I) in a series RLC circuit:

I = V_peak / √(R² + (ωL - 1 / (ωC))²)

Substituting the given values of peak voltage (6.0 mV), inductor resistance (0.28 Ω), and the resonant angular frequency (2 * π * f), where f is 1020 kHz, we find the peak current to be approximately 20.7 mA.

However, the current at 1020 kHz when the radio is tuned to a stronger station at 1200 kHz cannot be determined without additional information.

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The complete question is:

An AM radio antenna picks up a 1020 kHz signal with a peak voltage of 6.0 mV. The tuning circuit consists of a 70 μH inductor in series with a variable capacitor. The inductor coil has a resistance of 0.28 Ω and the resistance of the rest of the circuit is negligible.

Answer:

275000

Explanation:

momentum = mass * velocity

2500*110=275000

The force F1 is equal and opposite to the downward force thus, F1 is equal to 60 N. The force F2 is inclined to 30 ° from leftward force and it is equal to 38.97 N in magnitude.

Force is an external agent acting on a body to deform it or to change its state of motion or rest. Force is a vector quantity and it is characterised by its magnitude and direction.

If two forces acting on a body from the same directions, then the net force will be the sum of these two forces. If they are acting from opposite directions, they will cancel each other in magnitude.

The force F1 is equal and opposite to the force acting downward. Thus its magnitude is 60 N. The force F2 is inclined to 30 ° from horizontal direction.

F2 = 45 cos 30 = 38.9 N.

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Jupiter's diameter is km, and it completes one rotation of the axis in 9 hours, 56 minutes, producing a radial acceleration of 0.0337 m/s2 and an earth-g-force of 0.0337.

Think about landing on the surface if you could ( although in reality that would not be possible, because jupiter has no solid surface). Acceleration in mechanics refers to the rate of change in a moving object's velocity with respect to time. accelerations as a vector quantity. An object's acceleration with respect to a force depends on the direction of the net force acting on it. The following equation represents the radial acceleration:

Radial acceleration = (pi/T)

Radial acceleration is pi/(24 * 3600 * 2 * radius of the earth. 2 * 6.371 * 10^6)

Radial Acceleration is equal to 0.0337 m/s2.

Radial acceleration is equal to 3.43 * 10-3 g's.

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Answer:

60,000 J

Explanation:

The total Energy in the system = the sum of potential and kinetic energy

Total energy = K. E + P. E

K. E = 0.5mv²

m = mass ; v = velocity, K. E = kinetic energy

V = 20 m/s ; mass = 600kg

Total energy = 180000 J

Hence,

K. E = 0.5 * 600 * 20^2

K.E = 300 * 400

K. E = 120,000

P. E = TOTAL ENERGY - K.E

P.E = I80,000 - 120,000

P.E = 60,000 J

The acceleration is equal to the acceleration of gravity multiplied by the sine of the angle for a frictionless incline of degree.

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Answer:

The answer is "\(0.13562748\)"

Explanation:

Please find the complete question in the attached file.

Using formula:

\(\bold{U_s=\frac{v^2}{rg}}\)

Given:

\(r=1.60 \times 10^2 \ m\\\\g=9.8\\\\v= 52.5\ \frac{km}{hr}= 14.583\ \frac{m}{s}\)

put the value into the above-given formula:

\(U_s= \frac{14.583^2}{160 \times 9.8}\)

    \(= \frac{212.663889}{1568}\\\\=0.13562748\)

Answer:

100 m/s^{2}

Explanation:

the given information we have is:
vi = 30m/s

vf = 20m/s

t = 0.10s

we need to find a so we will use the following kinematics equation

\(vf=vi+at\)

we can rearrange the equation so it will give us our desired answer like so:

\(a = \frac{vf-vi}{t}\)

now we can plug in our given numbers

\(a = \frac{20 m/s - 30 m/s}{0.10s}\)

which will equal

\(100 m/s^{2}\)

Answer:

Here's a rough diagram for this question!

The scale I used is 1cm = 5000N.

So, 20000N = 4 cm & 30000N = 6cm.

To find the magnitude of the resultant force, draw a straight line from one corner of the parallelogram to the other end and measure the line. From the diagram, mine would be around 10cm. So, based on the scale I used, 10cm would be 50000N. Therefore, the resultant force is 50000N!

For the angle between the resultant force, I got around 13°-14°!

I hope this helps!

EDIT: My bad, I just noticed I wrote 2000N on my pic loll, thats supposed to be 20000N.

When a hydrogen atom forms a covalent link with an N, O, or F atom, hydrogen bonding takes place.

Only a few substances that contain hydrogen can form a hydrogen bond.

The hydrogen bonds in the CH4 molecule are visible.

When a F atom and a hydrogen atom are covalently bound, the hydrogen atom gains a slight positive charge.

Covalent bonds and hydrogen bonds are interchangeable terms.

The interaction known as hydrogen bonding, which involves a hydrogen atom sandwiched between two other atoms with a high affinity for electrons, is stronger than van der Waals forces but weaker than ionic or covalent bonds. Atoms in separate molecules or distinct regions of the same molecule can form hydrogen bonds with one another. A hydrogen atom (FH, NH, or OH) is covalently bound to one of the pair's (the donor) typically fluorine, nitrogen, or oxygen atoms, with which it shares electrons unevenly. As a result of this high electron affinity, the hydrogen gains a little positive charge. The other atom in the pair, which is usually F, N, or O, has an unshared electron pair, giving it a little negative charge.

The donor atom efficiently transfers its hydrogen to the receiver atom by electrostatic attraction, creating a connection. Water (H2O) is liquid over a much wider temperature range than would be anticipated for a molecule of its size due to its extensive hydrogen bonding. Because it quickly forms hydrogen bonds with the solute, water is an excellent solvent for ionic compounds as well as many other types of solutes. A linear protein molecule's ability to fold into its functional configuration depends on the hydrogen bonds formed between the amino acids. The double-helix structure of DNA is essential for the transmission of genetic information. It is created by hydrogen bonds between nitrogenous bases in nucleotides on the two strands of DNA (guanine partners with cytosine, adenine couples with thymine).

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Density is a measure of how much mass an object has in a unit of volume. It's determined by dividing the object's mass by its volume.

Density measurements are influenced by a variety of variables. In a laboratory environment, one of the most significant variables is the equipment used to obtain the measurements.

In a laboratory experiment, a 30 g sample and a 70 g sample were used to determine the density of a material. The 30 g sample is likely to have a larger percentage error than the 70 g sample.

The reason for this is as follows:

Because the mass of the 30 g sample is less than that of the 70 g sample, it will have a lower volume than the 70 g sample. Since the precision of volume measurements is influenced by the accuracy of the measuring equipment, the accuracy of volume measurements obtained for the 30 g sample is likely to be lower than that obtained for the 70 g sample. As a result, any error that occurs in the volume measurement will have a greater effect on the density calculation for the 30 g sample than for the 70 g sample.

As a result, the value obtained for the density of the 30 g sample is likely to have a larger percentage error than that found for the 70 g sample.

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The final distance traveled by the elevator is 60m and moved 36m (option B).

To calculate the total distance traveled by the elevator, we must take into account that each floor is equivalent to a distance of 3 meters.

So we need to multiply the number of floors he travels on each trip and multiply it by 3 to find the distance he traveled.

3m × 7 = 21m

3m × 4 = 12m

3m × 9 = 27m

To know the total distance traveled by the elevator, we must add the meters traveled in each displacement:

21m + 12m + 27m = 60m

On the other hand, to know the displacement that the elevator made from its initial position to its final position, we multiply 3 by the number of floors that there is a difference between its initial position and its final position.

3m × 12 = 36m

According to the above, it can be inferred that the correct answer is B. Because the elevator traveled a total of 60m and moved 36m.

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Explanation:

v= (f) x ( lambda)

1.7 ms^-1/12.05 m = f =o.14 hz

The calculate the total current through the circuit, we first need to understand the concept of series circuits.  Therefore, the total current through the circuit is 0.15 amps or 150 milliamps.

The four light bulbs are connected in series, which means that the current flowing through each bulb is the same. The total resistance of the circuit can be calculated by adding up the resistance of each bulb (10 ohms each) which gives us a total resistance of 40 ohms. Using Ohm's law, we can calculate the current flowing through the circuit by dividing the voltage of the battery (6.0 V) by the total resistance (40 ohms). This gives us a total current of 0.15 amps or 150 milliamps. Therefore, the total current through the circuit is 0.15 amps or 150 milliamps.

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Hypotheses

Null Hypothesis (H₀): The current ozone level is not significantly different from the normal level of 5.8 ppm.

Alternative Hypothesis (H₁): The current ozone level is significantly lower than the normal level of 5.8 ppm.

Z-test statistic

To calculate the z-test statistic, we use the formula:

z = (sample mean - population mean) / (standard deviation / √sample size)

Given:

Sample mean (x) = 5.7 ppm

Population mean (μ) = 5.8 ppm

Standard deviation (σ) = 1.1

Sample size (n) = 990

Plugging in the values:

z = (5.7 - 5.8) / (1.1 / √990)

z ≈ -2.28

Type of test

This is a one-tailed test. We are interested in whether the ozone level is significantly lower, not higher, than the normal level.

Decision rule

Since the significance level is 0.02, we reject the null hypothesis if the z-test statistic is less than the critical value corresponding to a 0.02 (2%) one-tailed significance level.

Conclusion

The z-test statistic value of -2.28 falls in the critical region and is less than the critical value for a 0.02 (2%) one-tailed test. Therefore, we reject the null hypothesis. The data supports the claim that the current ozone level is significantly lower than the normal level at the 0.02 level.

In summary, the data provides evidence to support the researcher's claim that the current ozone level is insufficient at a significance level of 0.02. The calculated z-test statistic of -2.28 falls in the critical region, leading to the rejection of the null hypothesis.

This suggests that there is a significant difference between the observed sample mean of 5.7 ppm and the expected population mean of 5.8 ppm. The ozone level appears to be lower than normal, warranting further attention and investigation.

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He magnitude of the average braking force is 12,000 N.

The braking force can be calculated using the following formula:

Now, let's use this formula to find the Braking force in each case based on the information of the chart:

Now, let's add the results and divide the result into three to find the average:

From these, the option that is the most similar is C 12,000 N

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The total energy of the body at evevry point is remained same due to the law of conservation of energy. Distance from A to B and final velocity of the ball just reach before C is 44.3 m/s.

d (distance) from A to B is = √2gh

In this case given are, g = 9.8 m/s² and h = 100m,

so here d = √(2⋅9.8⋅100) = 44.3m.

Final velocity ,v = √2gh

Here given are , v is the velocity, g is the acceleration due to gravity, and h is the height. In this case,

g = 9.8 m/s² ,h = 100m,

v = √(2⋅9.8⋅100)

= 44.3 m/s (final velocity)

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Designing a car that produces the lowest possible force on the dummy and does not injure the dummy in a 16 m/s crash requires a combination of weight reduction, aerodynamics, safety, and suspension design.

In the U.S., all cars are evaluated using a frontal 35 mph (~16 m/s) crash test. To design a car that produces the lowest possible force on the dummy and does not injure the dummy in a 16 m/s crash, the following steps can be followed:

Step 1: Weight reduction - The car's weight should be as low as possible while maintaining structural integrity. A lighter car will have a lower force during a crash. Therefore, using lightweight materials like aluminum can help reduce the weight of the car.

Step 2: Aerodynamics - Design the car to have the lowest coefficient of drag possible. A streamlined design will reduce the impact of the wind, which can cause a car to lose control at high speeds.

Step 3: Safety - The car should have an advanced safety system, such as airbags and seat belts, to protect the driver and passengers. The car's seat belts should be positioned correctly to protect the driver in a collision, and airbags should be installed to protect the driver's head and chest from impact.

Step 4: Suspension - The suspension system should be designed to absorb the force of a crash. A softer suspension system will absorb the impact of a collision, resulting in a lower force on the dummy.

Overall, designing a car that produces the lowest possible force on the dummy and does not injure the dummy in a 16 m/s crash requires a combination of weight reduction, aerodynamics, safety, and suspension design. By following these steps, it is possible to create a car that is both safe and efficient.

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Answer:

Average speed = 53.33 km/h

Explanation:

Below is the calculation for the average speed:

Given the average speed of for first 40 km = 80km/h

Time taken to cover the first 40 km = Total Distance / average speed

Time taken to cover the first 40 km = 40 / 80 = 0.5 hours

Given the average speed of for next 40 km = 40km/h

Time taken to cover the next 40 km = Total Distance / average speed

Time taken to cover the next 40 km = 40 / 40 = 1 hours

Now the average speed of the tuck to cover total distance:

Average speed = Total distance / Total time

Average speed = (40 + 40) / (0.5 + 1)

Average speed = 53.33 km/h

Answer:m=42kg

Explanation:

wieght = mass × gram

420 = mass × 10

therefore , answer is 42

Answer:

\(\huge \boxed{\mathrm{42 \ kg} }\)

Explanation:

\(\sf Weight \ (N) = mass \ (kg) \times acceleration \ of \ gravity \ (m/s^2)\)

\(\sf W=m \times g\)

We know that the acceleration of gravity on the Earth is approximately 10 m/s.

The weight of the body is given 420 N.

\(\sf 420=m \times 10\)

Solve for the mass. Divide both sides by 10.

\(\sf m = 42\)

The mass of the body is 42 kg.

Answer:

The ball travels faster when Mike throws it.

Explanation:

Mike throws the ball harder, with a greater force, so the ball travels faster when Mike throws it than when Joe does.

Answer:

5.03×10¯⁷ N

Explanation:

From the question given above, the following data were obtained:

Mass of the person (M₁) = 55 Kg

Mass of the car (M₂) = 1234 Kg

Distance apart (r) = 3 m

Gravitational constant (G) = 6.673×10¯¹¹ Nm²/Kg²

Force (F) =?

The force between the person and his car can be obtained as follow:

F = GM₁M₂ / r²

F = 6.673×10¯¹¹ × 55 × 1234 / 3²

F = 6.673×10¯¹¹ × 67870/ 9

F = 5.03×10¯⁷ N

Thus, the force between the person and his car is 5.03×10¯⁷ N

Answer:

I don't think so

Explanation:

Answer:

3a. 240 C

3b. 3666.67 A

Explanation:

3a. Determination of the charge.

Current (I) = 2 A

Time (t) = 120 s

Charge (Q) =?

The charge, current and time are related by the following equation:

Charge (Q) = current (I) × time (t)

Q = It

With the above formula, we can obtain the charge as follow:

Current (I) = 2 A

Time (t) = 120 s

Charge (Q) =?

Q = It

Q = 2 × 120

Q = 240 C

Thus, the charge is 240 C

3b. Determination of the current

We'll begin by converting 220 KC to C. This can be obtained as follow:

1 KC = 1000 C

Therefore,

220 KC = 220 KC × 1000 C / 1 KC

220 KC = 220000 C

Next, we shall express 1 minute in second. This is shown below:

1 min = 60 s

Finally, we shall determine the current. This can be obtained as follow:

Charge (Q) = 220000 C

Time (t) = 60 s

Current (I) =?

Q = It

220000 = I × 60

Divide both side by 60

I = 220000 / 60

I = 3666.67 A

Thus, the current flowing through the bulb is 3666.67 A

(a) The tension in the cable slanted at an angle of 38° is 90.32 N.

(b) The tension in the horizontal cable is 71.2 N.

The net force on the weight is determined by resolving the forces into x and y components as follows;

Let the rightward tension = T₁

Let the leftward tension = T₂

Sum of the horizontal forces is calculated as follows;

T₁cos(38) - T₂cos(0)  - 56 cos(90) = 0

0.788T₁ - T₂ = 0

0.788T₁ = T₂

Sum of the Vertical forces is calculated as follows;

T₁sin(38) + T₂sin(0) - 56sin(90) = 0

0.62T₁  - 56 = 0

T₁ = 56/0.62

T₁ = 90.32 N

The tension in the horizontal cable is calculated as follows;

T₂ = 0.788T₁

T₂ = 0.788 x 90.32 N

T₂ = 71.2 N

Thus, the tension in each cable is determined by resolving the forces into various components as shown above.

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