A ball is thrown at a height of 1.2m above the ground with an initial speed of 20 m/s at an angle 60 degrees above the horizontal. find a vector valued function r(t) describing the position of the ball

Answer: C

The Energy Independence and Security Act of 2007 mandates the use of more fuel efficient cars where car manufacturers are required to boost fleet wide gas mileage to 35 mp (14.8 km/l) by 2020 in order to help reduce petroleum consumption. It encourages the increase in fuel economy standards for passenger cars. Thus, promote production of fuel-efficient vehicles.  Additionally, the act also support the use of electric transportation technology. 

The answer is C. more fuel efficient car.s

The depth at which the pressure below the surface of a freshwater lake is 3.51 x 10^5 Pa is 24.29 meters.

The depth at which the pressure below the surface of a freshwater lake is 3.51 x 10^5 Pa can be calculated using the formula:

Pressure = atmospheric pressure + density of water * gravitational acceleration * depth

In this case, the atmospheric pressure is 1.01 x 10^5 Pa, the density of water is 1.00 x 10^3 kg/m^3, and the gravitational acceleration is 9.8 m/s^2. We can rearrange the equation to solve for depth:

Depth = (pressure - atmospheric pressure) / (density of water * gravitational acceleration)

Plugging in the values, we get:

Depth = (3.51 x 10^5 Pa - 1.01 x 10^5 Pa) / (1.00 x 10^3 kg/m^3 * 9.8 m/s^2)

Depth = 24.29 meters

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The work done by the electric field in moving a proton from +125V to -55V is -expressed as -180 electron volts (eV).

Using the relationship between work (W), charge (q), and electric potential difference (V).

The charge of a proton is +1.602 × 10^-19 coulombs (elementary charge, e), and the potential difference
V is the final potential minus the initial potential.

So, we compute the potential difference first:

V = V_final - V_initial = (-55V) - (+125V) = -180V

Then, we calculate the work done:

W = q
V = (1.602
10^-19 C)
(-180 V) = -2.8836
10^-17 joules

The negative sign indicates that the electric field is doing work against the electric potential. To express the work in electron volts, remember that 1 eV = 1.602
10^-19 joules:

W (in eV) = W (in joules) / (1.602
10^-19 joules/eV)
= (-2.8836
10^-17 joules) / (1.602
10^-19 joules/eV) = -180 eV

The expression for the velocity of a rider on the Ferris wheel after it has rotated through an angle [tex]\( \delta \theta \)[/tex] is given by:

[tex]\[ v = r \sqrt{2 \alpha \delta \theta} \][/tex]

To find the expression for the velocity of a rider after the Ferris wheel has rotated through an angle [tex]\( \delta \theta \)[/tex], we can use kinematic equations for rotational motion.

The kinematic equation relating angular displacement [tex](\( \delta \theta \))[/tex], initial angular velocity [tex](\( \omega_0 \))[/tex], angular acceleration [tex](\( \alpha \))[/tex], and time [tex](\( t \))[/tex] is:

[tex]\[ \delta \theta = \omega_0 t + \frac{1}{2} \alpha t^2 \][/tex]

Since the Ferris wheel starts from rest, [tex]\( \omega_0 = 0 \)[/tex], so the equation simplifies to:

[tex]\[ \delta \theta = \frac{1}{2} \alpha t^2 \][/tex]

We're interested in finding the angular velocity [tex](\( \omega \))[/tex] after the Ferris wheel has rotated through an angle [tex]\( \delta \theta \)[/tex]. To find [tex]\( \omega \)[/tex], we can use the kinematic equation relating angular displacement, initial angular velocity, angular acceleration, and final angular velocity:

[tex]\[ \omega^2 = \omega_0^2 + 2 \alpha \delta \theta \][/tex]

Since [tex]\( \omega_0 = 0 \)[/tex], this equation simplifies to:

[tex]\[ \omega^2 = 2 \alpha \delta \theta \][/tex]

Taking the square root of both sides:

[tex]\[ \omega = \sqrt{2 \alpha \delta \theta} \][/tex]

This gives us the angular velocity of the Ferris wheel after it has rotated through an angle [tex]\( \delta \theta \)[/tex].

However, to find the velocity of a rider at a particular point on the Ferris wheel, we need to convert this angular velocity to linear velocity. The linear velocity [tex](\( v \))[/tex] is related to the angular velocity [tex](\( \omega \))[/tex] by the equation:

[tex]\[ v = r \omega \][/tex]

Where:

- v is the linear velocity.

- r is the radius of the Ferris wheel.

So, substituting the expression for [tex]\( \omega \)[/tex] into this equation:

[tex]\[ v = r \sqrt{2 \alpha \delta \theta} \][/tex]

This is the expression for the velocity of a rider after the Ferris wheel has rotated through an angle [tex]\( \delta \theta \)[/tex].

The resistance of the radio circuit is 16.7 kΩ.

To calculate the resistance of the radio circuit when it operates at 3.0 volts and draws a current of 1.8 x 10-4 amperes, we can use Ohm's Law, which states that Resistance (R) equals Voltage (V) divided by Current (I), or R = V/I. Plugging in the given values, R = 3.0 V / (1.8 x 10-4 A), we find that the resistance is approximately 16,666.67 Ω, or 16.7 kΩ when rounded to three significant digits. When dealing with electrical circuits, it is important to understand concepts like resistance, voltage, and current, as they are fundamental to analyzing and predicting the behavior of the circuit.

Explanation:

The power of an electrical appliance is given by :

[tex]P=V\times I[/tex]

Where

V is the voltage source

I is the current flowing in the circuit

1. For 1200 W microwave, Current, I = 10.9 A

2. For 1500 W water heater, Current, I = 6.8 A    

3. For 100 W light bulb, Current, I = 0.9 A

4.  For 2000 W oven, Current, I = 9.1 A  

5. For 40 W light bulb, Current, I = 3.3 A      

Out of the above five appliances, the largest current is flowing in microwave and the smallest current is flowing in the light bulb.

So, the sequence from smallest current to the largest current is :

100 W light bulb ( 0.9 A) < 40 W light bulb (3.3 A) < 1500 W water heater (6.8 A) < 2000 W oven (9.1 A) < 1200 W microwave (10.9 A)

To find the vector position of the particle at any time t, use the kinematic equation r(t) = r0 + vit + 0.5at2. Plug in the values for the initial velocity and acceleration to get the position function.

Given that at time t, the particle has an acceleration of vector a = 2.00ĵ m/s2 and an initial velocity of vector vi = 9.00î m/s, we can find the vector position of the particle at any time t using the kinematic equations.

The position function is given by:

r(t) = r0 + vit + 0.5at2

Plugging in the values, we have:

r(t) = 0 + (9.00î m/s)(t) + 0.5(2.00ĵ m/s2)(t2)

So, the vector position of the particle at any time t is r(t) = 9.00tî + t2ĵ - t2 km.

Final answer:

Using the formula relating current, charge, and time, approximately 1.38 × 10^16 protons strike a target when 130 μA of current is directed at the target for 17.0 seconds.

Explanation:

To determine how many protons strike the target in 17.0 seconds with a current of 130 μA (microamperes), we must understand the relationship between electric current, charge, and the quantity of charged particles. Current (I) is defined as the amount of charge (Q) passing through a point in a circuit per unit of time (t), mathematically described by the equation I = Q/t. Given that each proton carries a charge of approximately 1.6 × 10-19 C (coulombs), we can find the total charge that strikes the target over 17.0 seconds and subsequently calculate the number of protons involved.

First, convert the current from microamperes to amperes: 130 μA = 130 × 10-6 A. Then, use I = Q/t to find the total charge Q: Q = I × t = (130 × 10-6 A) × 17.0 s = 2.21 × 10-3 C. Finally, calculate the number of protons by dividing the total charge by the charge of a single proton: Number of protons = Q / charge of one proton = (2.21 × 10-3 C) / (1.6 × 10-19 C/proton) ≈ 1.38 × 1016 protons.

Therefore, approximately 1.38 × 1016 protons strike the target in a period of 17.0 seconds.

Answer:

b

Explanation:

The water cycle is a biogeochemical cycle that is a closed system. the statement describes a viable stage that occur in water cycle is that water can change from solid to liquid at certain points in the cycle. therefore the correct answer is option B.

A dam or other construction that alters the natural flow of a river or other body of water is used to generate hydropower, often known as hydroelectric power.

Hydropower utilizes the endless water cycle, which uses water as fuel and produces no waste products, to produce electricity. Hydropower plants come in a variety of shapes and sizes, but they are always constantly pushed by the kinetic energy of water going downstream.

In a closed system, the water cycle is a biogeochemical cycle. The fact that water can transform from solid to liquid at specific periods during the cycle is described in the phrase as a possible stage that occurs in the water cycle.

Thus, the correct answer is option B.

Learn more about hydropower from here

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The correct answer is the frictional force.

In fact, the centripetal force is the force that keeps the car in circular motion, and it points toward the centre of the circular trajectory. The frictional force between the tyres of the car and the road provides the centripetal force that keeps the car in the turn: in fact, without the friction (e.g. on an icy road), the car would not be able to make the turn at the same speed.

Final answer:

The tension in the cable AB required to support the traffic light with a mass of 19 kg is equal to the weight of the traffic light, calculated as 186.2 N by multiplying the mass by the acceleration due to gravity.

Explanation:

To determine the tension in the cable AB required to support the traffic light with a mass of 19 kg, we need to use the concept that the tension must balance the weight of the traffic light. Since the traffic light is in equilibrium (not moving), the net force acting on it must be zero.

The weight of the traffic light (W) can be calculated using the formula W = m × g, where m is the mass of the traffic light and g is the acceleration due to gravity (which is approximately 9.8 m/s2 on the surface of the Earth).

Calculating the weight: W = 19 kg × 9.8 m/s2 = 186.2 N.

Now, since we are dealing with a situation where only one cable is mentioned and there are no angles provided, we assume the cable is vertical, and therefore, the tension in cable AB is simply the weight of the traffic light, which is 186.2 N.

the answer is C. it increases by a factor of 110, i got 100 on the test

When the light hits an opaque object, none of the light will pass through the object. Hence, option B is correct.

Electromagnetic radiation that the human eye can detect as light. From radio waves with wavelengths measured in meters to gamma rays with wavelengths shorter than roughly 1 1011 meter, electromagnetic radiation occurs throughout a very broad range of wavelengths.

The wavelengths of light that are visible to humans fall into a very small range within that wide spectrum, ranging from about 700 nanometers for red light to roughly 400 nm for violet light.

Infrared and ultraviolet are two spectral bands that are close to the visible region and are repeatedly alluded to as light as well.

Anything that doesn't let any light through is opaque. Instances of opaque materials include concrete, wood, and metal.

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Using the equation of motion v = u + gt and knowing that at the top of its trajectory the final velocity of the ball is 0, the time it takes to reach there is 0.5 seconds and the acceleration due to gravity is -9.8 m/s², we can determine the magnitude of the initial vertical component of the velocity to be 4.9 m/s. As the ball was thrown at a 30° angle, this means the magnitude of the initial velocity is 9.8 m/s.

In order to find the initial velocity of a projectile, we can use a foundational equation from Physics. Specifically, the formula v = u + gt where v is the final velocity, u is the initial velocity, g is acceleration due to gravity, and t is time. We're told that the ball takes 0.5 seconds to reach the top of its trajectory. At the top of its trajectory, the ball's final velocity will be 0 m/s (because it momentarily stops before falling back down). Also, the acceleration due to gravity is -9.8 m/s². Re-arranging the formula to solve for u gives us u = v - gt. Replacing v with 0, g with -9.8 m/s², and t with 0.5 s gives u = 0 - (-9.8 m/s² * 0.5s) = 4.9 m/s. However, this 4.9 m/s is just the vertical component of the initial velocity, because gravity acts vertically. Since the balls is thrown at an angle of 30°, to get the magnitude of the initial velocity, we have to divide 4.9 m/s by sin(30°) which gives us roughly 9.8 m/s. Therefore, the magnitude of the initial velocity is approximately 9.8 m/s.

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Answer:

hot plumes

Explanation:

The frequency of the wave is 4 Hz, the period is 1/4 seconds, the speed is 20 m/s, and the amplitude is 2 meters.

a. The frequency of the wave can be calculated by counting the number of complete vibrations in one second. In this case, the wave vibrates up and down four times each second, so the frequency is 4 Hz.

b. The period of the wave is the time it takes for one complete vibration. It can be calculated by taking the reciprocal of the frequency. In this case, the period is 1/4 seconds.

c. The speed of the wave can be determined by multiplying the frequency by the wavelength. Since the distance between two successive crests is 5 meters, the speed of the wave is 20 m/s.

d. The amplitude of the wave is the height from the lowest part to the highest part of the wave. In this case, the amplitude is 2 meters.

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Electric forces can act at a distance

Answer: This thing is a lever

Explanation: There isn't a picture, but I took the K12 class, so yeah

The simple machine with a rod fixed to the center of a wheel is a wheel and axle, which is a type of lever used to multiply applied force.

The simple machine pictured that consists of a rod fixed to the center of a wheel is known as a wheel and axle. This device is actually a form of lever where the force applied to the wheel results in a greater force being applied to the axle. It exemplifies how simple machines can be used to multiply or augment a force that we apply. The mechanical advantage is calculated by dividing the radius of the wheel by the radius of the axle.

The answer is C. Frictional charging is primarily involved. In the scenario, the bouquet of flowers represents a charged object that causes an electron (or the flower) to transfer from one object to another. Due to the bouquet of flowers, the other flower repelled and moved towards the object with a lesser charge.  As a result, the box becomes neutral or has no charge at all. 

The answer is D.

I just took the test and got it right

.

Answer:

I) You walk barefoot on the hot street and it burns your toes.

II) When you get into a car with hot black leather in the middle of the summer and your skin starts to get burned.

Explanation:

In conduction mode of heat transfer we know that the energy is transferred from one system to other system due to direct contact of two bodies

Here due to this direct contact the energy is transferred via a given solid or liquid medium

In this type of heat transfer medium particles will remain in its own position only the energy is transferred.

So here we can say the correct answer will be

I) You walk barefoot on the hot street and it burns your toes.

II) When you get into a car with hot black leather in the middle of the summer and your skin starts to get burned.