A Federation starship (8.5 ✕ 106 kg) uses its tractor beam to pull a shuttlecraft (1.0 ✕ 104 kg) aboard from a distance of 14 km away. The tractor beam exerts a constant force of 4.0 ✕104 N on the shuttlecraft. Both spacecraft are initially at rest. How far does the starship move as it pulls the shuttlecraft aboard?

Answer:

For a: The original speed of the truck is 4.76 m/s

For b: The acceleration of the truck is [tex]-0.23m/s^2[/tex]

Explanation:

Speed is defined as the rate at which an object moves with respect to time.

To calculate the time taken for the given speed, we use the equation:

[tex]s=\frac{d}{t}[/tex]

where,

s = speed of the truck

d = distance traveled = 40.0 m

t = time taken by truck = 8.50 s

Putting values in above equation, we get:

[tex]s=\frac{40.0m}{8.50s}=4.76m/s[/tex]

Hence, the original speed of the truck is 4.76 m/s

Acceleration is defined as the rate of change of velocity with respect to time.

Mathematically,

[tex]a=\frac{v-u}{t}[/tex]

where,

v = final velocity  of the truck = 2.80 m/s

u = initial velocity  of the truck = 4.76 m/s

t = time taken  = 8.50 s

Putting values in above equation, we get:

[tex]a=\frac{2.80-4.76}{8.50}=-0.23m/s^2[/tex]

Negative sign represents slowing down or deceleration.

Hence, the acceleration of the truck is [tex]-0.23m/s^2[/tex]

During the launch, the person was accelerating against the gravity, therefore the equation we use in this case is:

F = m * (g + a)

where m is mass = 60 kg, g is gravity = 9.81 m/s^2, a is acceleration = 4 * g

therefore:

F = m * (g + 4 g)

F = m * 5 g

F = 60 kg * 5 * (9.81 m/s^2)

F = 2943 N

The apparent weight of a 60 kg rider during the launch of a power tower ride experiencing 4g of acceleration is 2940 N. This is calculated by adding the force due to the rider's weight and the force due to the ride's acceleration.

To calculate the apparent weight of a rider during the launch, we need to consider the gravitational force (weight) and the additional force due to the 4g acceleration of the ride. The weight of the rider is calculated using the formula: Weight = Mass x Gravity, where mass is 60 kg and gravity is 9.8 m/s². This gives a weight of approximately 588 N (Newton).

The force due to the ride's acceleration is calculated using the formula: Force = Mass x Acceleration, where in this case acceleration is 4g or 4 x 9.8 m/s², which gives approximately 2352 N.

The apparent weight of the rider is therefore the sum of these two forces: 588 N + 2352 N = 2940 N.

So a 60 kg rider's apparent weight during the launch is 2940 N.

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Final answer:

To avoid hitting the ledge when jumping from a cliff, calculate the time of flight using the height of the cliff and gravity, then use that time to find the minimum horizontal velocity needed to clear the ledge width.

Explanation:

Minimum Speed to Miss the Ledge

To find the minimum speed required for a person to miss the ledge when jumping from a cliff, one must analyze the motion in two dimensions: vertical and horizontal. The vertical distance (h) and the width of the ledge (w) are crucial to determine the time in the air and the minimum horizontal velocity needed.

The vertical motion is independent of the horizontal motion and can be analyzed using the formula for the time of flight under gravity which is t = [tex]\sqrt(2h/g)[/tex], where g is the acceleration due to gravity. Once the time of flight is calculated, we use this time to find the minimum horizontal velocity (vmin) necessary to travel the width of the ledge w by the formula vmin = w/t. This is the minimum speed the person needs just as they leave the edge of the cliff.

For a ledge 1.75m wide and cliff 8.00m high, first, calculate the time of flight with t = [tex]\sqrt((2*8.00m)/9.81m/s2)[/tex]. Then, use this time to calculate the horizontal velocity with v min = 1.75m / t.

Answer:

(a) 33.52 m/s

(b) 16.46 m/s downward

Explanation:

To find the initial speed of the rocket, we can use the kinematic equation:

[tex]v = u + at[/tex]

where:

In this case:

Therefore:

[tex]10 = u + (-9.8)(2.4)[/tex]

[tex]10 = u - 23.52[/tex]

[tex]u = 10 + 23.52[/tex]

[tex]u = 33.52 \textsf{ m/s}[/tex]

So, the speed of the rock at launch is 33.52 m/s.

We can use the same kinematic equation to find the speed at t = 5.1 s:

[tex]v = u + at[/tex]

[tex]v = 33.52 + (-9.8)(5.1)[/tex]

[tex]v = 33.52 - 49.98[/tex]

[tex]v = -16.46 \textsf{ m/s}[/tex]

The negative sign indicates that the rock is moving downward at this time.

So, 5.1 seconds after launch, the speed of the rock is 16.46 m/s downward.

Answer:

Theories are not opinions.

Explanation:

Theories are all of them tested, with the scientific method in order to be accepted or refuted, then Laws are tested and are observable by any means all around the globe, the only option that is actually correct would be that Theories are not opinions because they are scientific statements that can be tested.

Answer:

theories are not opinions

Explanation:

Final answer:

Explanation of calculating the distance between two deer in a field using trigonometry and the Pythagorean theorem.

Explanation:

Given information:

Deer b is 64.9 m from deer a at an angle of 53.4° north of west. Deer c is 77.9 m north of east relative to deer a. The distance between deer b and c is 96.8 m.

To find: Distance between deer a and c.

Calculation:

Using trigonometry, we can find the distances and then apply the Pythagorean theorem to calculate the distance between deer a and c.

Distance between deer a and c is approximately 59.2 meters.

We have that the magnitude of the electric force that the proton exerts on the electron

[tex]F=5.45*10^{-10}N[/tex]

From the question we are told that

proton and an electron are separated by 6.5 Ã 10â10 m

Generally the equation for the Force  is mathematically given as

[tex]F=\frac{kq_1q_2}{r^2}\\\\F=\frac{9*10^{9}*(1.6*10^{-19})^2}{(6.5*10^{-10})^2}[/tex]

[tex]F=5.45*10^{-10}N[/tex]

Therefore

the magnitude of the electric force that the proton exerts on the electron

[tex]F=5.45*10^{-10}N[/tex]

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The following situation occurs:

The two objects are brought close to each other (but they do not touch). Object B must be negatively charged: in this case, for induction, the positive charges on object A migrate towards the side of the object closer to object B, while the negative charges migrate to the other side. Then, object A must be connected to the ground, so that the negative charges migrate to the ground: therefore, an excess of positive charges remain on object A, which is now positively charged.

Answer:

a positive charge will transfer from object b

Explanation:

a positive charge will transfer from object b to object a making a positively charged

Have a good day = )

Answer : Distance, d = 40 mi.

Explanation :

It is given that,

Fiora starts riding her bike at 20 mi/h. after a while, she slows down to 12 mi/h and maintains that speed for the rest of the trip. the whole trip of 70 mi takes her 4.5 h.

Let for t hours she traveled at 20 mi/h. So, for ( 4.5 - t) h she has traveled with a speed of 12 mi/h.

We know that,

distance covered = speed × time

20 mi/h × t +12 mi/h (4.5 h - t) = 70 mi

t = 2 h

So, the distance covered in 2 h is, d = 20 mi/h × 2 h = 40 mi.

Hence, this is the required solution.

Considering a box sitting in the back of a pickup. The pickup accelerates to the right, and because the bed of the pickup is sticky, the box does not slide around the truck when this happens. But the force acting on the box is left.

Force is responsible for the motion of an object. it produces acceleration in the body. According to newton's second law force is mass times acceleration i.e. F =ma. Its SI unit is N which is equivalent to kg.m/s².

There are two types of forces, balanced force and unbalanced force.

When Net force acting on a body is zero then we call it as balanced force. .

Unbalanced forces are those when resultant of all the forces is not equal to zero is called as unbalanced force. unbalanced force is responsible for the motion of the body.

Whatever we are talking about force in this problem is called as pseudo force, it same as we feel in the bus when we are standing in the bus suddenly driver brakes we go ahead in the bus or we feel forward force.

Pseudo force is not actual force but it can felt, centrifugal force is a type of pseudo force.

In this problem, as pickup accelerates, according to newtons first law box in the pickup tend to have its original velocity(0 if pickup is at rest or v when it is in motion). because of this when pickup accelerates right, box feel pseudo force in the opposite direction(Left).

Hence left is correct.

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Final answer:

The chemical formula for mercury(I) nitrate is Hg2(NO3)2, featuring a Hg₂²+ dimeric cation.

Explanation:

The chemical formula for mercury(I) nitrate is Hg2(NO3)2. This compound is created when a large excess of mercury reacts with dilute nitric acid. Mercury(I) compounds are unique because they contain a Hg₂²+ ion, which is a dimeric cation where two mercury atoms are bonded together, each with a +1 oxidation state, giving the overall molecule a +2 charge. It's important to note that the compound must be handled with care due to the toxicity of mercury compounds.

By replacing a 40 W incandescent bulb with an 8 W LED bulb and leaving the lights on for 24 hours, you would be saving 768 Wh of energy per day.

The question is asking how much energy you can save by switching from a 40 W incandescent lightbulb to an 8 W LED bulb. The energy use of a bulb is determined by its power (wattage) and the time it is turned on. To calculate the energy saved, we need to compare the energy use of the two different bulbs, when they are turned on for the same time.

Step 1: We start by calculating the daily energy consumption of the 40 W incandescent light bulb. Energy (E) in watt-hours (Wh) can be calculated using the formula E = P*t, where P is the power in watts (W) and t is the time in hours. Therefore, for the 40 W incandescent bulb used 24 hours a day: E1 = 40 W * 24 hours = 960 Wh/day.

Step 2: Then we calculate the daily energy consumption of the 8 W LED bulb. For the LED bulb: E2 = 8 W * 24 hours = 192 Wh/day.

Step 3: To find the daily amount of energy saved, we subtract the energy use of the LED bulb from the energy use of the incandescent bulb: E saved = E1 - E2 = 960 Wh/day - 192 Wh/day = 768 Wh/day. Therefore, by replacing a 40 W incandescent lightbulb with an 8 W LED bulb and leaving the lights on for 24 hours a day, you can save 768 Wh of energy each day.

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a force must act on it

Archimedes' principle states that a completely submerged object always displaces its own volume of water, creating an upward buoyant force.

In physics, an object that is completely submerged underwater will always displace its own volume of water.

This is known as Archimedes' principle, which states that the buoyant force acting on an object is equal to the weight of the fluid it displaces.

For example, if a 1 liter object is submerged in water, it will displace 1 liter of water. This displacement results in an upward force, called the buoyant force, that opposes the weight of the object.

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The percent uncertainty in this question refers to how much measured values could deviate from a standard or expected value. For this example, considering a good-quality measuring tape that can be off by 0.50cm over a distance of 20m, the percent uncertainty is calculated as 0.0025%

The concept this question is referring to is percent uncertainty, which is a quantitative measure of how much measured values deviate from a standard or expected value. It's widely used in physics and engineering. In a practical context, when you're using a measuring tape, it's unlikely you'll get a perfect measurement every time. This could be due to factors like the smallest division on the tape or the person using it having bad eyesight. In this particular example, measuring tape error was 0.50 cm over a distance of 20 m (or 2000 cm).

The percent uncertainty is calculated by dividing the uncertainty (the amount the measurement could be off by) by the measured value, and then multiplying by 100% to express it as a percentage.

So, percent uncertainty = (uncertainty/measured value) * 100%.
For this scenario, percent uncertainty = (0.50 cm / 20000 cm) * 100% which equals to 0.0025%.

So, in this example, the percent uncertainty is 0.0025%.

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The percent uncertainty of the measuring tape is 0.025%.

To find the percent uncertainty of a measurement, you use the following formula:

[tex]\text{Percent Uncertainty} = \left( \frac{\text{Absolute Uncertainty}}{\text{Measured Value}} \right) \times 100 \%[/tex]

Given:

First, convert the Measured Value to centimeters because the absolute uncertainty is given in centimeters.

[tex]20 \text{ m} = 2000 \text{ cm}[/tex]

Now, plug the values into the formula:

[tex]\text{Percent Uncertainty} = \left( \frac{0.50 \text{ cm}}{2000 \text{ cm}} \right) \times 100 \%[/tex]

Calculate the result:

[tex]\text{Percent Uncertainty} = \left( \frac{0.50}{2000} \right) \times 100 \% = 0.025 \%[/tex]

The maximum height is: hmax  = v0² sin² α / 2 g
The horizontal range is: x = v0² sin 2 α / g

So we are given that:

x = 14.5 hmax

v0² sin 2 α / g = 14.5 v0² sin² α / 2 g
7.25 sin² α = 2 sin α cos α    
7.25 sin α = 2 cos α  
7.25 tan α = 2
tan α = 0.27586
α = tan^(-1) 0.27586
α = 15.42°
The angle of projection is 15.42°