A tennis ball traveling horizontally at 22.0 m/s suddenly hits a vertical brick wall and bounces back with a horizontal velocity of 18.0 m/s

The maximum altitude reached by the rocket is 334.2 meters, and the total time elapsed from takeoff until the rocket strikes the ground is 16.55 seconds.

To find the maximum altitude reached by the rocket, we need to consider two stages: the powered ascent and the free-fall descent. During the powered ascent, the rocket accelerates upwards at a constant acceleration of 52.7 m/s2 for 1.41 seconds.

Using the kinematic equation for displacement: s = ut + (1/2)at2, where 's' is displacement, 'u' is initial velocity (0 m/s in this case, as it starts from rest), 'a' is acceleration, and 't' is time, we get:

s = 0 m/s * 1.41 s + 0.5 * 52.7 m/s2 * (1.41 s)2 = 52.3 meters

Now, the velocity at the end of the powered ascent can be found using the equation v = u + at, giving us v = 0 m/s + 52.7 m/s2 * 1.41 s = 74.3 m/s. This is the initial velocity for the free-fall ascent.

For the free-fall, the only acceleration is due to gravity, which is -9.81 m/s2 (negative as it opposes the initial velocity). We use v2 = u2 + 2as to find the additional altitude gained in free-fall when the velocity reaches zero (v = 0 m/s at the maximum height). Solving for 's', we get:

s = (0 m/s)2 - (74.3 m/s)2 / (2 * -9.81 m/s2) = 281.9 meters

So, the total maximum altitude is the sum of the displacement during the powered ascent and the additional altitude gained in free-fall which is 52.3 meters + 281.9 meters = 334.2 meters.

To find the total time elapsed until the rocket strikes the ground, we'll add the time of ascent, the time to reach maximum altitude during free-fall, and the time it takes to fall back down from that altitude. We've already found the time of ascent (1.41 s) and can use the same velocity and acceleration to find the time to reach maximum altitude during free-fall with the formula t = (v - u) / a, giving us t = (0 m/s - 74.3 m/s) / -9.81 m/s2 = 7.57 s. For the descent, the time from maximum altitude to the ground will be equal to twice the time from the end of powered ascent to maximum altitude, since the paths are the same and the final velocities (at the ground) will be equal in magnitude but opposite in direction.

The total time elapsed from takeoff until the rocket strikes the ground is then 1.41 s + 2 * 7.57 s = 16.55 seconds.

Kinetic energy is the energy that is possessed by an object that is moving. It is calculated by one-half the product of the mass and the square of the velocity of the object. We calculate as follows:

KE = mv^2 / 2
KE = 908 kg (89 km/hr ( 1000 m / 1 km) ( 1 hr / 3600 s ))^2 / 2
KE = 277479.48 J or 204658.05 ft-lbf

Final answer:

The alpha star in a constellation is generally the brightest within that constellation, as designated by the Bayer system, using Greek letters such as Alpha Centauri or Alpha Orionis for Betelgeuse.

Explanation:

The alpha star in a constellation is named using a system introduced by Johann Bayer in 1603, which designates stars with Greek letters according to their brightness within that constellation. The alpha star is typically the brightest star in its constellation. For example, Alpha Centauri is the brightest star in the Centaurus constellation, visible from south of the equator. Similarly, Alpha Orionis, or Betelgeuse, is the brightest star in the Orion constellation. Stars like Sirius, Vega, and Altair also fall under this naming system. Apparent brightness is subject to change over long periods due to stars' space velocity, making certain stars more prominent in our skies at different times.

The designation of stars within a constellation also serves astronomy and celestial navigation, highlighting important features of the celestial sphere. Not all stars within the vicinity of the Sun are equally visible or as bright, with only a few within 26 light-years appearing among the brightest in our sky. The alpha designation helps us identify and catalogue these celestial bodies systematically.

D: Neither ultrasonic nor infrasonic vibrations can be heard by humans.

Answer

D. Neither ultrasonic nor infrasonic vibrations can be heard by humans.

Explanation

Human hearing is somehow limited. Frequencies below 20 Hz cannot be heard by human and sounds of frequencies above 20,000 Hz too. The sounds of frequency below 20 Hz are known as the infrasonic sounds. Those above 20,000 Hz are called Ultrasonic sounds.

time = distance/speed

Final answer:

The time required to make a 4400-km trip across the United States, averaging 80 km/h, is 55 hours.

Explanation:

To calculate the time required for a trip, the formula you use is time (t) equals the distance (d) divided by the average speed (v), often expressed as t = d / v. In this case, the distance of the trip is 4400 kilometers, and the average speed is 80 kilometers per hour (km/h). Therefore, the time required for the trip is calculated as follows:

Distance (d) = 4400 km

Average speed (v) = 80 km/h

Time (t) = Distance ÷ Average speed

Time (t) = 4400 km ÷ 80 km/h

Time (t) = 55 hours

The trip would take 55 hours if you average 80 km/h.

Pamela can drive 121,333,212 kilometers with 121212 liters of fuel, given her car's fuel efficiency is 1001 kilometers per liter.

Pamela drove her car 999999 kilometers using 999 liters of fuel. She wants to know how many kilometers (k) she can drive with 121212 liters of fuel, assuming the relationship between kilometers and fuel is proportional.

To find the number of kilometers she can drive with 121212 liters of fuel, we first need to determine her car's fuel efficiency, which is:

Fuel Efficiency (km per liter) = 999999 km / 999 liters = 1001 km per liter

Next, we use this fuel efficiency to calculate the distance she can drive with 121212 liters of fuel:

Distance (k) = Fuel Efficiency × Amount of Fuel

Distance (k) = 1001 km per liter × 121212 liters = 121333212 kilometers

Therefore, Pamela can drive 121,333,212 kilometers with 121212 liters of fuel.

Answer: A. How the soil particles clump together

Explanation:

Solid part of the soil clumps together. There are air pores between the soil particles. This determines the soil structure. The soil takes the shape based on the its physical and chemical properties. The main four types of soil structure are:  

1. Columns

2. Blocky

3. Granular

4. Plate-like

It has decreased by a factor of four

The intensity of the wave has increased by a factor of four.

The amount of visible light emitted per unit solid angle in time. Lumens are the measurements of how much light is emitted from a source in a given second (also known as luminous power or luminous flux). The luminosity is assessed in relation to visual perception.

The inverse Square Law of Light states that light intensity falls off rapidly with distance from its source. The intensity varies with the square of the flash-to-subject distance.

( Intensity at distance 1 ) / ( Intensity at distance 2 )

= ( Distance₂²/ Distance₁² )

In our case, Distance₁=10m and Distance₂=20m, which means that the intensity of the wave has increased by a factor of four. The ratio will be calculated as:-

20²/10²= 400/100=4,

Therefore, the intensity of the wave has increased by a factor of four.

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Final answer:

When approaching a yellow light at an intersection, the safest approach is to slow down and prepare to stop unless stopping is unsafe or impossible due to proximity. Traffic engineers take into account the 'no-win' zone to minimize the chances of an accident. Speeding up to beat the yellow light increases the risk of accidents and is not recommended.

Explanation:

Safest Approach at a Yellow Light

When you encounter a yellow light at an intersection, the safest and legally correct approach is to prepare to stop if it is safe to do so. A yellow light is a warning that the light will soon turn red. You should only proceed through the intersection if you are already so close to it that stopping would be unsafe or impossible due to the short stopping distance. It is not advisable to speed up to try to ‘beat’ the yellow light, as this can increase the risk of accidents.

Understanding Traffic Engineer Considerations

Traffic engineers design the duration of the yellow light to minimize what is known as the “no-win” zone. This is a position too far from the light to pass through the intersection before the light turns red, and too close to safely stop without entering the intersection. The appropriate “yellow time” is calculated to allow drivers in most situations to either pass through the intersection safely or to stop in time.

Special Circumstances

There can be circumstances where a driver might assess the situation differently, such as the example of driving a pregnant woman to the hospital at 4am with no other cars around. However, legally and typically for safety, the best action is to prepare to stop when you see a yellow light.

Answer:

220

Explanation:e2020

Answer:

The Horizontal component of initial velocity (V0x) must be 28.18 m/s.

Explanation:

Vertical distance = y = 50m    

Horizontal distance = x = 90 m  

We know that,

x = x0 + V0xt  

where,

x0 = Initial distance in horizontal direction = 0  

V0x = x/t = 90/t          ……… (i)

As,  

y = y0 + V0y + ½ gt^2

where,

y0 = Initial distance in vertical direction = 0

V0y = Vertical component of initial velocity = 0

So,

t = √(50)(2)/(9.8)

t = 3.194 s

Put t = 3.194 s in equation (i),

V0x = 90/3.194

V0x = 28.18 m/s

Answer:

1. Increased

2. 340

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Explanation:

Answer:

Final pressure of he gas is 0.3 atm.

Explanation:

It is given that,

Initial pressure of the gas, P₁ = 1.2 atm

Initial volume of the gas, V₁ = 1 L

Final volume of the gas, V₂ = 4 L

We need to find the final pressure of the gas. It can be calculated using Boyle's law as :

[tex]P_1V_1=P_2V_2[/tex]

[tex]P_2=\dfrac{P_1V_1}{V_2}[/tex]

[tex]P_2=\dfrac{1.2\ atm\times 1\ L}{4\ L}[/tex]

[tex]P_2=0.3\ atm[/tex]

So, the final pressure of the gas at constant temperature is 0.3 atm. Hence, this is the required solution.

The gravitational effect on other bodies determines the weight (or the mass) of a planet. We must somehow measure the strength of its "tug" on another object in order to use gravity to find the mass of a planet. We can harness Newton's equations to deduce what the mass of the planet must be through observing the time it takes for the satellite to orbit its primary planet.

Given:

Mass of Venus = 4.87 x 1024 kg

= 4986.88

Mass of Jupiter = 1.898 x 1024 kg

= 1943.552

Mass of Jupiter compared to mass of Venus

1943.552 / 4986.88

= 0.3897330595482546

= 0.3897330595482546 x 100%

= 38.97%

So, in this problem, the mass of Jupiter is about 0.39 times the mass of Venus.

Final answer:

The neutral load demand for a 25 kW electric range may be considered negligible or zero for calculations unless the manufacturer's documentation indicates otherwise, due to typically being a pure 240V appliance with balanced legs.

Explanation:

The neutral load demand for an electric range rated at 25 kW will depend on whether the range is designed for a balanced three-phase power supply or a single-phase power supply. In a residential setting in the United States, it is typically single-phase. For many electric ranges, the neutral only carries the imbalance current, which is the difference between the two hot legs of a 240V circuit. However, if the range uses 120V components such as lights or controls, the neutral would carry that load as well. If we assume a pure 240V appliance with no 120V components and perfect balance, there would be no current on the neutral. In practice, there might be some load on the neutral, but for the purpose of this question and the majority of calculations for residential service, we often consider it to be negligible or zero for a large 240V appliance like a 25 kW range, unless specified by the manufacturer's documentation.

Refraction of sound waves occurs when there are temperature differences in the air, causing the sound waves to change direction due to changes in speed.

Refraction of sound waves often takes place when there are temperature differences in the air. This is option A of the student's question. The phenomenon of refraction in sound occurs when sound waves travel from one medium to another medium with a difference in temperature. This causes a change in the speed of sound wave, leading to a change in direction, or refraction. For instance, during a hot day, the air near the ground is hotter than the air above. Here, the speed of sound is faster closer to the ground, causing the sound waves to bend upwards.

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Ans: 8 hours and 90 minutes

The length of Football field = 300ft by 160 ft.

On converting it into meter, we get length of field = 91.44 m

and the width of field = 48.8 m 

Now, distance = Area moved/ width = (91.44*48.8) / 0.5 = 8924.55 m = 8.9245 km

Ans, Time taken = distance*speed = 8.9245*1 km/hr = 8 hours and 90 minutes

It would take approximately 8.96 hours for one person to mow a football field with a lawn mower that has a 0.5 meter width and moves at a speed of 1 km/hr.

To estimate how long it would take one person to mow a football field using an ordinary home lawn mower, let's look at the size of an American football field and the capacity of a standard lawn mower. An American football field is 100 yards long, not including the end zones. Since 1 yard is approximately 0.9144 meters, the length of the field is about 91.44 meters. The width of a football field is 53.3 yards, which is about 48.77 meters.

Now, considering the mower has a 0.5 meter width and moves with a speed of 1 km/hour, which equals 0.2778 meters/second (since 1 km/h equals 0.2778 m/s), it is referred to when doing calculations for velocity or speed, we need to convert the dimensions and the speed to compatible units.

The area of the football field can be calculated as 91.44 meters in length multiplied by 48.77 meters in width, resulting in approximately 4460.09 square meters. Now, we will find out how many strips of 0.5 meter width are needed to cover the width of the field: 48.77 meters / 0.5 meters = 97.54, which we round up to 98 passes. Since each pass covers a length of 91.44 meters, a single pass would take 91.44 meters / 0.2778 meters/second = 329.25 seconds. Multiplying this by the number of passes gives us the time to mow the entire field: 329.25 seconds/pass × 98 passes = 32,266.5 seconds, or approximately 8.96 hours.

The fastest way to reach maximum braking capability, whether with or without ABS, is to firmly and rapidly apply the brakes. If the car has an ABS, the system would automatically prevent the wheels from locking up, but without it, the driver should manually pump the brakes.

The fastest way to reach maximum braking capability, whether your vehicle contains the Anti-lock Braking System (ABS) or not, is to blast the brakes. This method is about firmly and rapidly applying the brake pedal. With ABS, the system takes over and prevents the wheels from locking up, while without ABS, the driver should pump the brakes to avoid wheel lock up. However, keep in mind that in both cases, keep your steering wheel steady and do not turn it abruptly.

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The fastest way to reach maximum braking capability is to apply the brakes as hard as possible without locking up the wheels, either manually or with ABS.

The fastest way to reach maximum braking capability with or without ABS is to apply the brakes as hard as possible without locking up the wheels. This creates the maximum friction between the tires and the road, allowing the vehicle to decelerate quickly.

With ABS (Anti-lock Braking System), the braking system automatically modulates the brake pressure to prevent wheel lock-up, ensuring that the tires remain in contact with the road and maximizing braking efficiency.

Without ABS, the driver needs to manually pump the brakes to prevent wheel lock-up. This allows the tires to maintain traction and achieve maximum braking capability.

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We can determine the object with more mass by applying equal force to both objects, the more massive object will accelerate less.

According to Newton's second law of motion, the force applied to an object is directly proportional to the product of the mass and acceleration of the object.

F = ma

[tex]a = \frac{F}{m}[/tex]

where;

At equal force, the object with less mass will accelerate more.

Thus, we can determine the object with more mass by applying equal force to both objects, the more massive object will accelerate less.

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